Question 1

Find  f′(x) f^{\prime}(x) f′(x)   for the function, then find  f′(x) f^{\prime}(x) f′(x)   for the given  xxx .
- f(x) =8x+2,f′(0) f(x) =\frac{8}{x+2}, f^{\prime}(0) f(x) =x+28​,f′(0)

Accepted Answer

A)    f′(x) =−8(x+2) 2;f′(0) =−2f^{\prime}(x) =-\frac{8}{(x+2) ^{2}} ; f^{\prime}(0) =-2f′(x) =−(x+2) 28​;f′(0) =−2 
B)    f′(x) =4(x+2) 2;f′(0) =1f^{\prime}(x) =\frac{4}{(x+2) ^{2}} ; f^{\prime}(0) =1f′(x) =(x+2) 24​;f′(0) =1 
C)    f′(x) =−4(x+2) 2;f′(0) =−1f^{\prime}(x) =-\frac{4}{(x+2) ^{2}} ; f^{\prime}(0) =-1f′(x) =−(x+2) 24​;f′(0) =−1 
D)    f′(x) =8(x+2) 2;f′(0) =2f^{\prime}(x) =\frac{8}{(x+2) ^{2}} ; f^{\prime}(0) =2f′(x) =(x+2) 28​;f′(0) =2E) A) and B)
F) A) and C)

Question 2

Find all points where the function is discontinuous.
-

Accepted Answer

A)    x=2x=2x=2 
B)    x=4x=4x=4 
C)    x=4,x=2x=4, x=2x=4,x=2 
D)   None E) None of the above
F) A) and B)

Question 3

Find the equation of the tangent line to the curve when  x\mathbf{x}x  has the given value.
- f(x) =4x;x=5\mathrm{f}(\mathrm{x}) =\frac{4}{\mathrm{x}} ; \mathrm{x}=5f(x) =x4​;x=5

Accepted Answer

A)    y=13x−16y=13 x-16y=13x−16 
B)    y=−39x−80y=-39 x-80y=−39x−80 
C)    y=−4x25+85y=-\frac{4 x}{25}+\frac{8}{5}y=−254x​+58​ 
D)    y=x20+15y=\frac{x}{20}+\frac{1}{5}y=20x​+51​E) A) and B)
F) A) and C)

Question 4

Find the equation of the tangent line to the curve when  x\mathbf{x}x  has the given value.
- f(x) =x5;x=4f(x) =\frac{\sqrt{x}}{5} ; x=4f(x) =5x​​;x=4

Accepted Answer

A)    y=−4x25+85y=-\frac{4 x}{25}+\frac{8}{5}y=−254x​+58​ 
B)    y=−39x−80y=-39 x-80y=−39x−80 
C)    y=13x−16y=13 x-16y=13x−16 
D)    y=x20+15y=\frac{x}{20}+\frac{1}{5}y=20x​+51​E) A) and B)
F) A) and C)

Question 5

Solve the problem.
-The total revenue from the sale of  xxx  stereos is given by  R(x) =1000(1−x300) 2R(x) =1000\left(1-\frac{x}{300}\right) ^{2}R(x) =1000(1−300x​) 2 . Find the average revenue from the sale of  xxx  stereos.

Accepted Answer

A)    R(x) =1000x(1−x300) 2R(x) =\frac{1000}{x}\left(1-\frac{x}{300}\right) ^{2}R(x) =x1000​(1−300x​) 2 
B)    R(x) =500x(1−x300) 2R(x) =500 x\left(1-\frac{x}{300}\right) ^{2}R(x) =500x(1−300x​) 2 
C)    R(x) =1000x(1−x300) 2R(x) =1000 x\left(1-\frac{x}{300}\right) ^{2}R(x) =1000x(1−300x​) 2 
D)    R(x) =500x(1−x300) 2R(x) =\frac{500}{x}\left(1-\frac{x}{300}\right) ^{2}R(x) =x500​(1−300x​) 2E) A) and D)
F) B) and C)

Question 6

Find the derivative.
- y=4ex2y=4 e^{x^{2}}y=4ex2

Accepted Answer

A)    8xe4x28 x e^{4 x^{2}}8xe4x2 
B)    8xe2x8 x e^{2 x}8xe2x 
C)    8xe8 x \mathrm{e}8xe 
D)    8xex28 x e^{x^{2}}8xex2E) C) and D)
F) B) and D)

Question 7

Use the properties of limits to evaluate the limit if it exists.
- lim⁡x→12x−74x+5\lim _{x \rightarrow 1} \frac{2 x-7}{4 x+5}limx→1​4x+52x−7​

Accepted Answer

A)    −12-\frac{1}{2}−21​ 
B)    −75-\frac{7}{5}−57​ 
C)    −59-\frac{5}{9}−95​ 
D)   Does not exist E) None of the above
F) A) and C)

Question 8

Find functions  ggg  and  hhh  such that  f(x) =g(h(x) ) f(x) =g(h(x) ) f(x) =g(h(x) )  .
- f(x) =e6x+8f(x) =e^{6 x+8}f(x) =e6x+8

Accepted Answer

A)    g(x) =ln⁡x,h(x) =6x+8g(x) =\ln x, h(x) =6 x+8g(x) =lnx,h(x) =6x+8 
B)    g(x) =e6x,h(x) =x+8g(x) =e^{6 x}, h(x) =x+8g(x) =e6x,h(x) =x+8 
C)    g(x) =ex,h(x) =6x+8g(x) =e^{x}, h(x) =6 x+8g(x) =ex,h(x) =6x+8 
D)    g(x) =6x+8,h(x) =exg(x) =6 x+8, h(x) =e^{x}g(x) =6x+8,h(x) =exE) All of the above
F) B) and D)

Question 9

Solve the problem.
-The cost of manufacturing a particular videotape (in dollars)  is  c(x) =9000+8xc(x) =9000+8 xc(x) =9000+8x , where  xxx  is the number of tapes produced. The average cost per tape (in dollars) , denoted by  cˉ(x) \bar{c}(x) cˉ(x)  , is found by dividing  c(x) \mathrm{c}(\mathrm{x}) c(x)   by  x\mathrm{x}x . Find  lim⁡x→1000c‾(x) \lim _{\mathrm{x} \rightarrow 1000} \overline{\mathrm{c}}(\mathrm{x}) limx→1000​c(x)  .

Accepted Answer

A)    $24\$ 24$24 
B)    $17\$ 17$17 
C)    $10\$ 10$10 
D)   does not exist E) None of the above
F) A) and B)

Question 10

Find the derivative of the function.
- y=x2−4(2x−1) 2y=\frac{x^{2}-4}{(2 x-1) ^{2}}y=(2x−1) 2x2−4​

Accepted Answer

A)    y′=−2x−4(4x−1) 3y^{\prime}=-\frac{2 x-4}{(4 x-1) ^{3}}y′=−(4x−1) 32x−4​ 
B)    y′=−2x+16(2x−1) 3y^{\prime}=-\frac{2 x+16}{(2 x-1) ^{3}}y′=−(2x−1) 32x+16​ 
C)    y′=−2x(2x−1) 3y^{\prime}=-\frac{2 x}{(2 x-1) ^{3}}y′=−(2x−1) 32x​ 
D)    y′=2x2+16(2x−1) 3y^{\prime}=\frac{2 x^{2}+16}{(2 x-1) ^{3}}y′=(2x−1) 32x2+16​E) B) and C)
F) B) and D)

Question 11

Use the limit properties to find the following limit.
-If  lim⁡x→1f(x) =10\lim _{x \rightarrow 1} f(x) =10limx→1​f(x) =10  and  lim⁡x→1g(x) =3\lim _{x \rightarrow 1} g(x) =3limx→1​g(x) =3 , find  lim⁡x→1f(x) g(x) \lim _{x \rightarrow 1} \frac{f(x) }{g(x) }limx→1​g(x) f(x) ​ .

Accepted Answer

A)   -1
B)    103\frac{10}{3}310​ 
C)    −103-\frac{10}{3}−310​ 
D)   Does not exist E) B) and D)
F) B) and C)

Question 12

Find the derivative.
- f(x) =ln⁡xexf(x) =\frac{\ln x}{e^{x}}f(x) =exlnx​

Accepted Answer

A)    1−xln⁡xex\frac{1-x \ln x}{e^{x}}ex1−xlnx​ 
B)    1xex\frac{1}{x e^{x}}xex1​ 
C)    ln⁡xxex\frac{\ln x}{x e^{x}}xexlnx​ 
D)    1−xln⁡xxex\frac{1-x \ln x}{x e^{x}}xex1−xlnx​E) A) and B)
F) C) and D)

Question 13

Solve the problem.}
-A car rental firm charged  $30\$ 30$30  per day or portion of a day to rent a car for a period of 1 to 4 days. Days 5 to 8 were then "free," while the charge for days 9 through 15 was again  $30\$ 30$30  per day. Let  C(t) C(t) C(t)   represent the total cost to rent the car for  ttt  days, where   15 . Find the total cost of a rental for 3 days.

Accepted Answer

A)    $30\$ 30$30 
B)    $90\$ 90$90 
C)    $120\$ 120$120 
D)    $33\$ 33$33E) B) and D)
F) A) and B)

Question 14

Provide the proper response.
-A particle has a position function  s(t) s(t) s(t)  . Is the derivative of  s(t) s(t) s(t)   with respect to time at a given time  t1t_{1}t1​ , the average or instantaneous velocity?

Accepted Answer

A)  A verage Velocity
B)   Neither
C)  I nstantaneous velocity
D)   Both E) B) and D)
F) B) and C)

Question 15

Find the following.
- f′(4) f^{\prime}(4) f′(4)   if  f(x) =9x5/2−7x3/2f(x) =9 x^{5 / 2}-7 x^{3 / 2}f(x) =9x5/2−7x3/2

Accepted Answer

A)   96
B)   6
C)   8
D)   159 E) C) and D)
F) A) and D)

Question 16

Find the point from those given that has the given property.
-The point where the slope of the tangent is least

Accepted Answer

A)    (0,0) (0,0) (0,0)  
B)    (−1,−1) (-1,-1) (−1,−1)  
C)    (1,3) (1,3) (1,3) D) A) and B)
E) All of the above

Question 17

The graph shows the total sales in thousand of dollars from the distribution of x thousand catalogs. Find the average rate of change of sales with respect to the number of catalogs distributed for the change in x.
 
-10 to 30

Accepted Answer

A)   3
B)    23\frac{2}{3}32​ 
C)    13\frac{1}{3}31​ 
D)   1 E) A) and B)
F) A) and C)

Question 18

Find  f[g(x) ]f[g(x) ]f[g(x) ]  and  g[f(x) ]g[f(x) ]g[f(x) ] .
- f(x) =x+5;g(x) =4x−1f(x) =\sqrt{x+5} ; g(x) =4 x-1f(x) =x+5​;g(x) =4x−1

Accepted Answer

A)    f[g(x) ]=4x2+1f[g(x) ]=\sqrt{4 x^{2}+1}f[g(x) ]=4x2+1c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​  g[f(x) ]=4x2−5g[f(x) ]=\sqrt{4 x^{2}-5}g[f(x) ]=4x2−5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    f[g(x) ]=2x+1f[g(x) ]=2 \sqrt{x+1}f[g(x) ]=2x+1c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​  g[f(x) ]=4x+5−1g[f(x) ]=4 \sqrt{x+5}-1g[f(x) ]=4x+5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​−1 
C)    f[g(x) ]=2x+5f[g(x) ]=2 \sqrt{x+5}f[g(x) ]=2x+5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​  g[f(x) ]=4x+1−1g[f(x) ]=4 \sqrt{x+1}-1g[f(x) ]=4x+1c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​−1 
D)    f[g(x) ]=4x2−5f[g(x) ]=\sqrt{4 x^{2}-5}f[g(x) ]=4x2−5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​  g[f(x) ]=4x2−5g[f(x) ]=\sqrt{4 x^{2}-5}g[f(x) ]=4x2−5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​E) None of the above
F) A) and D)

Question 19

Find  f[g(x) ]f[g(x) ]f[g(x) ]  and  g[f(x) ]g[f(x) ]g[f(x) ] .
- f(x) =7/(x) 4;g(x) =2x3f(x) =7 /(x) ^{4} ; g(x) =2 x^{3}f(x) =7/(x) 4;g(x) =2x3

Accepted Answer

A)   f[g(x) ]=7/16x12\mathrm{f}[\mathrm{g}(\mathrm{x}) ]=7 / 16 \mathrm{x} 12f[g(x) ]=7/16x12  g[f(x) ]=686/(x) 12g[f(x) ]=686 /(x) ^{12}g[f(x) ]=686/(x) 12 
B)    f[g(x) ]=7x12/16f[g(x) ]=7 x^{12} / 16f[g(x) ]=7x12/16  g[f(x) ]=x12/686\mathrm{g}[\mathrm{f}(\mathrm{x}) ]=\mathrm{x}^{12 / 686}g[f(x) ]=x12/686 
C)    f[g(x) ]=7x12/686f[g(x) ]=7 x^{12} / 686f[g(x) ]=7x12/686  g[f(x) ]=x12/16\mathrm{g}[\mathrm{f}(\mathrm{x}) ]=\mathrm{x}^{12 / 16}g[f(x) ]=x12/16 
D)    f[g(x) ]=686/7x12f[g(x) ]=686 / 7 x^{12}f[g(x) ]=686/7x12  g[f(x) ]=16/(x) 12\mathrm{g}[\mathrm{f}(\mathrm{x}) ]=16 /(\mathrm{x}) ^{12}g[f(x) ]=16/(x) 12E) None of the above
F) B) and C)

Question 20

Let  f(x) =8x2−5xf(x) =8 x^{2}-5 xf(x) =8x2−5x  and  g(x) =7x+9g(x) =7 x+9g(x) =7x+9 . Find the composite.
- f[g(k) ]\mathrm{f}[\mathrm{g}(\mathrm{k}) ]f[g(k) ]

Accepted Answer

A)    392k2+973k+603392 k^{2}+973 k+603392k2+973k+603 
B)    392k2−973k+603392 k^{2}-973 k+603392k2−973k+603 
C)    56k2+35k+956 k^{2}+35 k+956k2+35k+9 
D)    56k2−35k+956 k^{2}-35 k+956k2−35k+9E) B) and C)
F) B) and D)

Exam 11: Differential Calculus

Find the derivative of the function. - $y=\frac{x^{2}-4}{(2 x-1) ^{2}}$

Correct Answer
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Find functions $g$ and $h$ such that $f(x) =g(h(x) )$ . - $f(x) =e^{6 x+8}$

Correct Answer
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Solve the problem. -The total revenue from the sale of $x$ stereos is given by $R(x) =1000\left(1-\frac{x}{300}\right) ^{2}$ . Find the average revenue from the sale of $x$ stereos.

Correct Answer
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Use the properties of limits to evaluate the limit if it exists. - $\lim _{x \rightarrow 1} \frac{2 x-7}{4 x+5}$

Correct Answer
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Find the derivative. - $y=4 e^{x^{2}}$

Correct Answer
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Find $f[g(x) ]$ and $g[f(x) ]$ . - $f(x) =7 /(x) ^{4} ; g(x) =2 x^{3}$

Correct Answer
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Correct Answer
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Find $f^{\prime}(x)$ for the function, then find $f^{\prime}(x)$ for the given $x$ . - $f(x) =\frac{8}{x+2}, f^{\prime}(0)$

Correct Answer
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Use the limit properties to find the following limit. -If $\lim _{x \rightarrow 1} f(x) =10$ and $\lim _{x \rightarrow 1} g(x) =3$ , find $\lim _{x \rightarrow 1} \frac{f(x) }{g(x) }$ .

Correct Answer
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Find the equation of the tangent line to the curve when $\mathbf{x}$ has the given value. - $\mathrm{f}(\mathrm{x}) =\frac{4}{\mathrm{x}} ; \mathrm{x}=5$

Correct Answer
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Find all points where the function is discontinuous. -

Correct Answer
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Find the point from those given that has the given property. -The point where the slope of the tangent is least

Correct Answer
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Find $f[g(x) ]$ and $g[f(x) ]$ . - $f(x) =\sqrt{x+5} ; g(x) =4 x-1$

Correct Answer
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Provide the proper response. -A particle has a position function $s(t)$ . Is the derivative of $s(t)$ with respect to time at a given time $t_{1}$ , the average or instantaneous velocity?

Correct Answer
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Correct Answer
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Let $f(x) =8 x^{2}-5 x$ and $g(x) =7 x+9$ . Find the composite. - $\mathrm{f}[\mathrm{g}(\mathrm{k}) ]$

Correct Answer
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Find the equation of the tangent line to the curve when $\mathbf{x}$ has the given value. - $f(x) =\frac{\sqrt{x}}{5} ; x=4$

Correct Answer
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Find the following. - $f^{\prime}(4)$ if $f(x) =9 x^{5 / 2}-7 x^{3 / 2}$

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Find the derivative. - $f(x) =\frac{\ln x}{e^{x}}$

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Exam 11: Differential Calculus

Find the derivative of the function. - y=x2−4(2x−1) 2y=\frac{x^{2}-4}{(2 x-1) ^{2}}y=(2x−1) 2x2−4​

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Find functions ggg and hhh such that f(x) =g(h(x) ) f(x) =g(h(x) ) f(x) =g(h(x) ) . - f(x) =e6x+8f(x) =e^{6 x+8}f(x) =e6x+8

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Solve the problem. -The total revenue from the sale of xxx stereos is given by R(x) =1000(1−x300) 2R(x) =1000\left(1-\frac{x}{300}\right) ^{2}R(x) =1000(1−300x​) 2 . Find the average revenue from the sale of xxx stereos.

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Use the properties of limits to evaluate the limit if it exists. - lim⁡x→12x−74x+5\lim _{x \rightarrow 1} \frac{2 x-7}{4 x+5}limx→1​4x+52x−7​

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Find the derivative. - y=4ex2y=4 e^{x^{2}}y=4ex2

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Find f[g(x) ]f[g(x) ]f[g(x) ] and g[f(x) ]g[f(x) ]g[f(x) ] . - f(x) =7/(x) 4;g(x) =2x3f(x) =7 /(x) ^{4} ; g(x) =2 x^{3}f(x) =7/(x) 4;g(x) =2x3

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Find f′(x) f^{\prime}(x) f′(x) for the function, then find f′(x) f^{\prime}(x) f′(x) for the given xxx . - f(x) =8x+2,f′(0) f(x) =\frac{8}{x+2}, f^{\prime}(0) f(x) =x+28​,f′(0)

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Use the limit properties to find the following limit. -If lim⁡x→1f(x) =10\lim _{x \rightarrow 1} f(x) =10limx→1​f(x) =10 and lim⁡x→1g(x) =3\lim _{x \rightarrow 1} g(x) =3limx→1​g(x) =3 , find lim⁡x→1f(x) g(x) \lim _{x \rightarrow 1} \frac{f(x) }{g(x) }limx→1​g(x) f(x) ​ .

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Find the equation of the tangent line to the curve when x\mathbf{x}x has the given value. - f(x) =4x;x=5\mathrm{f}(\mathrm{x}) =\frac{4}{\mathrm{x}} ; \mathrm{x}=5f(x) =x4​;x=5

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Find all points where the function is discontinuous. -

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Find the point from those given that has the given property. -The point where the slope of the tangent is least

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Find f[g(x) ]f[g(x) ]f[g(x) ] and g[f(x) ]g[f(x) ]g[f(x) ] . - f(x) =x+5;g(x) =4x−1f(x) =\sqrt{x+5} ; g(x) =4 x-1f(x) =x+5​;g(x) =4x−1

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Provide the proper response. -A particle has a position function s(t) s(t) s(t) . Is the derivative of s(t) s(t) s(t) with respect to time at a given time t1t_{1}t1​ , the average or instantaneous velocity?

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The graph shows the total sales in thousand of dollars from the distribution of x thousand catalogs. Find the average rate of change of sales with respect to the number of catalogs distributed for the change in x. -10 to 30

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Let f(x) =8x2−5xf(x) =8 x^{2}-5 xf(x) =8x2−5x and g(x) =7x+9g(x) =7 x+9g(x) =7x+9 . Find the composite. - f[g(k) ]\mathrm{f}[\mathrm{g}(\mathrm{k}) ]f[g(k) ]

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Find the equation of the tangent line to the curve when x\mathbf{x}x has the given value. - f(x) =x5;x=4f(x) =\frac{\sqrt{x}}{5} ; x=4f(x) =5x​​;x=4

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Find the following. - f′(4) f^{\prime}(4) f′(4) if f(x) =9x5/2−7x3/2f(x) =9 x^{5 / 2}-7 x^{3 / 2}f(x) =9x5/2−7x3/2

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Find the derivative. - f(x) =ln⁡xexf(x) =\frac{\ln x}{e^{x}}f(x) =exlnx​

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Find the derivative of the function. - $y=\frac{x^{2}-4}{(2 x-1) ^{2}}$

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Find functions $g$ and $h$ such that $f(x) =g(h(x) )$ . - $f(x) =e^{6 x+8}$

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Solve the problem. -The total revenue from the sale of $x$ stereos is given by $R(x) =1000\left(1-\frac{x}{300}\right) ^{2}$ . Find the average revenue from the sale of $x$ stereos.

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Use the properties of limits to evaluate the limit if it exists. - $\lim _{x \rightarrow 1} \frac{2 x-7}{4 x+5}$

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Find the derivative. - $y=4 e^{x^{2}}$

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Find $f[g(x) ]$ and $g[f(x) ]$ . - $f(x) =7 /(x) ^{4} ; g(x) =2 x^{3}$

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Find $f^{\prime}(x)$ for the function, then find $f^{\prime}(x)$ for the given $x$ . - $f(x) =\frac{8}{x+2}, f^{\prime}(0)$

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Use the limit properties to find the following limit. -If $\lim _{x \rightarrow 1} f(x) =10$ and $\lim _{x \rightarrow 1} g(x) =3$ , find $\lim _{x \rightarrow 1} \frac{f(x) }{g(x) }$ .

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Find the equation of the tangent line to the curve when $\mathbf{x}$ has the given value. - $\mathrm{f}(\mathrm{x}) =\frac{4}{\mathrm{x}} ; \mathrm{x}=5$

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Find $f[g(x) ]$ and $g[f(x) ]$ . - $f(x) =\sqrt{x+5} ; g(x) =4 x-1$

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Provide the proper response. -A particle has a position function $s(t)$ . Is the derivative of $s(t)$ with respect to time at a given time $t_{1}$ , the average or instantaneous velocity?

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Let $f(x) =8 x^{2}-5 x$ and $g(x) =7 x+9$ . Find the composite. - $\mathrm{f}[\mathrm{g}(\mathrm{k}) ]$

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Find the equation of the tangent line to the curve when $\mathbf{x}$ has the given value. - $f(x) =\frac{\sqrt{x}}{5} ; x=4$

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Find the following. - $f^{\prime}(4)$ if $f(x) =9 x^{5 / 2}-7 x^{3 / 2}$

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Find the derivative. - $f(x) =\frac{\ln x}{e^{x}}$

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