Question 1

Use the limit process to find the slope of the graph of  x+4\sqrt { x + 4 }x+4​  at  (5,3) ( 5,3 ) (5,3)  .

Accepted Answer

A)    13\frac { 1 } { 3 }31​ 
B)   3
C)    ∞\infty∞ 
D)    16\frac { 1 } { 6 }61​ 
E)   the slope is undefined at this point

Question 2

Use the limit process to find the slope of the graph of  6x−4x2 6 x-4 x^{2} 6x−4x2  at  (7,−154)  (7,-154)  (7,−154)  .

Accepted Answer

A)    -2 
B)   62
C)   34
D)   56
E)   -50

Question 3

Use the first six terms to predict the limit of the sequence  an=5n3+8n+3a _ { n } = \frac { 5 n ^ { 3 } + 8 } { n + 3 }an​=n+35n3+8​  (assume  nnn  begins with 1 ) .

Accepted Answer

A)    53\frac { 5 } { 3 }35​ 
B)   111
C)   79
D)   0
E)   the sequence diverges

Question 4

Consider the following graph of the function and approximate  lim⁡x→0e−4x−1x\lim _ { x \rightarrow 0 } \frac { e ^ { - 4 x } - 1 } { x }limx→0​xe−4x−1​ , if it exists.

Accepted Answer

A)    −1- 1−1 
B)    −4- 4−4 
C)   0
D)   1
E)   The limit does not exist.

Question 5

Use the figure below to approximate the slope of the curve at the point  (x,y) ( x , y ) (x,y)  .

Accepted Answer

A)   2
B)    32\frac { 3 } { 2 }23​ 
C)    −2- 2−2 
D)    −1- 1−1 
E)   1

Question 6

Use the limit process to find the slope of the graph of  x+21 \sqrt{x+21} x+21​  at  (4,5)  (4,5)  (4,5)  .

Accepted Answer

A)    15 \frac{1}{5} 51​ 
B)   5
C)    ∞ \infty ∞ 
D)    110 \frac{1}{10} 101​ 
E)   the slope is undefined at this point

Question 7

Using the summation formulas and properties, evaluate the following expression.
 ∑i=1604\sum _ { i = 1 } ^ { 60 } 4∑i=160​4

Accepted Answer

A)   7320
B)   1830
C)   236
D)   240
E)   64

Question 8

Find the following limit.
 lim⁡x→−43x2+3x+1\lim _ { x \rightarrow - 4 } 3 x ^ { 2 } + 3 x + 1limx→−4​3x2+3x+1

Accepted Answer

A)   52
B)   36
C)   37
D)    −23- 23−23 
E)    −35- 35−35

Question 9

Determine any points on the graph of the following function at which the tangent line is horizontal.  f(x) =x2+6x−8f ( x )  = x ^ { 2 } + 6 x - 8f(x) =x2+6x−8

Accepted Answer

A)    (3,19) ( 3,19 ) (3,19)  
B)    (3,0) ( 3,0 ) (3,0)  
C)    (−3,0) ( - 3,0 ) (−3,0)  
D)    (1,−1) ( 1 , - 1 ) (1,−1)  
E)    (−3,−17) ( - 3 , - 17 ) (−3,−17)

Question 10

Find
 lim⁡x→85xx+2\lim _ { x \rightarrow 8 } \frac { 5 x } { \sqrt { x + 2 } }limx→8​x+2​5x​ 
by direct substitution.

Accepted Answer

A)    810\frac { 8 } { \sqrt { 10 } }10c-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'/>​8​ 
B)    10210 \sqrt { 2 }102c-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'/>​ 
C)    401040 \sqrt { 10 }4010c-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'/>​ 
D)   1
E)    4010\frac { 40 } { \sqrt { 10 } }10c-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'/>​40​

Question 11

Use asymptotes to match   f(x) =4x2x2+1f(x) =\frac{4 x^{2}}{x^{2}+1}f(x) =x2+14x2​  with its graph.

Accepted Answer

A)  
B)  
C)   
D)  
E)

Question 12

Complete the table and use the result to estimate     lim⁡x→−3x+3x2−x−12\lim _{x ightarrow-3} \frac{x+3}{x^{2}-x-12}limx→−3​x2−x−12x+3​   numerically.
 x−3.1−3.01−3.001−3−2.999−2.99−2.9f(x) ?\begin{array}{|c|c|c|c|c|c|c|c|}\hline x & -3.1 & -3.01 & -3.001 & -3 & -2.999 & -2.99 & -2.9 \\hline f(x)  & & & & ? & & & \\hline\end{array}xf(x) ​−3.1​−3.01​−3.001​−3?​−2.999​−2.99​−2.9​​

Accepted Answer

A)    −17 -\frac{1}{7} −71​ 
B)   7
C)    ∞ \infty ∞ 
D)    −7 -7 −7 
E)   limit does not exist

Question 13

Use the function below and its derivative to determine any points on the graph of  f f f  at which the tangent line is horizontal.
 f(x) =3x4−6x2,f′(x) =12x3−12xf(x) =3 x^{4}-6 x^{2}, \quad f^{\prime}(x) =12 x^{3}-12 xf(x) =3x4−6x2,f′(x) =12x3−12x

Accepted Answer

A)    (−1,−3) ,(0,0) ,(1,−3)  (-1,-3) ,(0,0) ,(1,-3)  (−1,−3) ,(0,0) ,(1,−3)  
B)    (−1,3) ,(1,12)  (-1,3) ,(1,12)  (−1,3) ,(1,12)  
C)    (−1,−3) ,(1,−3)  (-1,-3) ,(1,-3)  (−1,−3) ,(1,−3)  
D)    (0,0) ,(1,0)  (0,0) ,(1,0)  (0,0) ,(1,0)  
E)    (0,0) ,(1,−3)  (0,0) ,(1,-3)  (0,0) ,(1,−3)

Question 14

Use the graph to find  lim⁡x→34x2−36x−3\lim _ { x \rightarrow 3 } \frac { 4 x ^ { 2 } - 36 } { x - 3 }limx→3​x−34x2−36​ .

Accepted Answer

A)   24
B)    ∞\infty∞ 
C)   12
D)   0
E)   limit does not exist

Question 15

Find  lim⁡h→0f(x+h) −f(x) h\lim _ { h \rightarrow 0 } \frac { f ( x + h )  - f ( x )  } { h }limh→0​hf(x+h) −f(x) ​  for  f(x) =2+6xf ( x )  = 2 + 6 xf(x) =2+6x .

Accepted Answer

A)    −6- 6−6 
B)    −4- 4−4 
C)   6
D)   2
E)   limit does not exist

Question 16

Find an equation of the tangent line to the graph of the following function at the point  (−1,−5)  (-1,-5)  (−1,−5)  
 −3x2−2 -3 x^{2}-2 −3x2−2

Accepted Answer

A)    y=6x−11 y=6 x-11 y=6x−11  
B)    y=6x+11 y=6 x+11 y=6x+11 
C)    y=6x+1 y=6 x+1 y=6x+1 
D)    y=30x−25 y=30 x-25 y=30x−25 
E)    y=30x+25 y=30 x+25 y=30x+25

Question 17

Find the following limit, if it exists.
 lim⁡x→−39−3x−2x23+x\lim _ { x \rightarrow - 3 } \frac { 9 - 3 x - 2 x ^ { 2 } } { 3 + x }limx→−3​3+x9−3x−2x2​

Accepted Answer

A)    −3- 3−3 
B)   9
C)   7
D)    −11- 11−11 
E)   The limit does not exist.

Question 18

Find  lim⁡x→−∞[x(7+x) 2−6]\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( 7 + x )  ^ { 2 } } - 6 \right]limx→−∞​[(7+x) 2x​−6]  (if it exists) .

Accepted Answer

A)    −549- \frac { 5 } { 49 }−495​ 
B)   6
C)    −6- 6−6 
D)    ∞\infty∞ 
E)   limit does not exist

Question 19

Consider the following graph of the function and approximate  lim⁡x→0e−4x−1x\lim _ { x \rightarrow 0 } \frac { e ^ { - 4 x } - 1 } { x }limx→0​xe−4x−1​ , if it exists.

Accepted Answer

A)    −1- 1−1 
B)    −4- 4−4 
C)   0
D)   1
E)   The limit does not exist.

Question 20

Find
 lim⁡x→64xx+4\lim _ { x \rightarrow 6 } \frac { 4 x } { \sqrt { x + 4 } }limx→6​x+4​4x​ 
by direct substitution.

Accepted Answer

A)    610\frac { 6 } { \sqrt { 10 } }10c-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'/>​6​ 
B)    464 \sqrt { 6 }46c-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'/>​ 
C)    241024 \sqrt { 10 }2410c-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'/>​ 
D)   1
E)    2410\frac { 24 } { \sqrt { 10 } }10c-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'/>​24​

Exam 11: Calculus Practice Problems

Find an equation of the tangent line to the graph of the following function at the point $(-1,-5)$ $-3 x^{2}-2$

Correct Answer
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Correct Answer
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Correct Answer
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Find $\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( 7 + x ) ^ { 2 } } - 6 \right]$ (if it exists) .

Correct Answer
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Using the summation formulas and properties, evaluate the following expression. $\sum _ { i = 1 } ^ { 60 } 4$

Correct Answer
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Find the following limit, if it exists. $\lim _ { x \rightarrow - 3 } \frac { 9 - 3 x - 2 x ^ { 2 } } { 3 + x }$

Correct Answer
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Use the graph to find $\lim _ { x \rightarrow 3 } \frac { 4 x ^ { 2 } - 36 } { x - 3 }$ . $Use the graph to find \lim _ { x \rightarrow 3 } \frac { 4 x ^ { 2 } - 36 } { x - 3 } . A) 24 B) \infty C) 12 D) 0 E) limit does not exist$

Correct Answer
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Complete the table and use the result to estimate $\lim _{x \rightarrow-3} \frac{x+3}{x^{2}-x-12}$ numerically. $\begin{array}{|c|c|c|c|c|c|c|c|}\hline x & -3.1 & -3.01 & -3.001 & -3 & -2.999 & -2.99 & -2.9 \\\hline f(x) & & & & ? & & & \\\hline\end{array}$

Correct Answer
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Find $\lim _ { x \rightarrow 8 } \frac { 5 x } { \sqrt { x + 2 } }$ by direct substitution.

Correct Answer
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Use the figure below to approximate the slope of the curve at the point $( x , y )$ . $Use the figure below to approximate the slope of the curve at the point ( x , y ) . A) 2 B) \frac { 3 } { 2 } C) - 2 D) - 1 E) 1$

Correct Answer
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Use the first six terms to predict the limit of the sequence $a _ { n } = \frac { 5 n ^ { 3 } + 8 } { n + 3 }$ (assume $n$ begins with 1 ) .

Correct Answer
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Use the limit process to find the slope of the graph of $\sqrt { x + 4 }$ at $( 5,3 )$ .

Correct Answer
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Find $\lim _ { x \rightarrow 6 } \frac { 4 x } { \sqrt { x + 4 } }$ by direct substitution.

Correct Answer
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Use the function below and its derivative to determine any points on the graph of $f$ at which the tangent line is horizontal. $f(x) =3 x^{4}-6 x^{2}, \quad f^{\prime}(x) =12 x^{3}-12 x$

Correct Answer
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Use asymptotes to match $f(x) =\frac{4 x^{2}}{x^{2}+1}$ with its graph.

Correct Answer
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Find the following limit. $\lim _ { x \rightarrow - 4 } 3 x ^ { 2 } + 3 x + 1$

Correct Answer
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Use the limit process to find the slope of the graph of $\sqrt{x+21}$ at $(4,5)$ .

Correct Answer
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Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ for $f ( x ) = 2 + 6 x$ .

Correct Answer
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Determine any points on the graph of the following function at which the tangent line is horizontal. $f ( x ) = x ^ { 2 } + 6 x - 8$

Correct Answer
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Use the limit process to find the slope of the graph of $6 x-4 x^{2}$ at $(7,-154)$ .

Correct Answer
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Exam 11: Calculus Practice Problems

Find an equation of the tangent line to the graph of the following function at the point (−1,−5) (-1,-5) (−1,−5) −3x2−2 -3 x^{2}-2 −3x2−2

Correct AnswerverifiedShow Answer

Consider the following graph of the function and approximate lim⁡x→0e−4x−1x\lim _ { x \rightarrow 0 } \frac { e ^ { - 4 x } - 1 } { x }limx→0​xe−4x−1​ , if it exists.

Correct AnswerverifiedShow Answer

Consider the following graph of the function and approximate lim⁡x→0e−4x−1x\lim _ { x \rightarrow 0 } \frac { e ^ { - 4 x } - 1 } { x }limx→0​xe−4x−1​ , if it exists.

Correct AnswerverifiedShow Answer

Find lim⁡x→−∞[x(7+x) 2−6]\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( 7 + x ) ^ { 2 } } - 6 \right]limx→−∞​[(7+x) 2x​−6] (if it exists) .

Correct AnswerverifiedShow Answer

Using the summation formulas and properties, evaluate the following expression. ∑i=1604\sum _ { i = 1 } ^ { 60 } 4∑i=160​4

Correct AnswerverifiedShow Answer

Find the following limit, if it exists. lim⁡x→−39−3x−2x23+x\lim _ { x \rightarrow - 3 } \frac { 9 - 3 x - 2 x ^ { 2 } } { 3 + x }limx→−3​3+x9−3x−2x2​

Correct AnswerverifiedShow Answer

Use the graph to find lim⁡x→34x2−36x−3\lim _ { x \rightarrow 3 } \frac { 4 x ^ { 2 } - 36 } { x - 3 }limx→3​x−34x2−36​ .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find lim⁡x→85xx+2\lim _ { x \rightarrow 8 } \frac { 5 x } { \sqrt { x + 2 } }limx→8​x+2​5x​ by direct substitution.

Correct AnswerverifiedShow Answer

Use the figure below to approximate the slope of the curve at the point (x,y) ( x , y ) (x,y) .

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Use the first six terms to predict the limit of the sequence an=5n3+8n+3a _ { n } = \frac { 5 n ^ { 3 } + 8 } { n + 3 }an​=n+35n3+8​ (assume nnn begins with 1 ) .

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Use the limit process to find the slope of the graph of x+4\sqrt { x + 4 }x+4​ at (5,3) ( 5,3 ) (5,3) .

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Find lim⁡x→64xx+4\lim _ { x \rightarrow 6 } \frac { 4 x } { \sqrt { x + 4 } }limx→6​x+4​4x​ by direct substitution.

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Use the function below and its derivative to determine any points on the graph of f f f at which the tangent line is horizontal. f(x) =3x4−6x2,f′(x) =12x3−12xf(x) =3 x^{4}-6 x^{2}, \quad f^{\prime}(x) =12 x^{3}-12 xf(x) =3x4−6x2,f′(x) =12x3−12x

Correct AnswerverifiedShow Answer

Use asymptotes to match f(x) =4x2x2+1f(x) =\frac{4 x^{2}}{x^{2}+1}f(x) =x2+14x2​ with its graph.

Correct AnswerverifiedShow Answer

Find the following limit. lim⁡x→−43x2+3x+1\lim _ { x \rightarrow - 4 } 3 x ^ { 2 } + 3 x + 1limx→−4​3x2+3x+1

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Use the limit process to find the slope of the graph of x+21 \sqrt{x+21} x+21​ at (4,5) (4,5) (4,5) .

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Find lim⁡h→0f(x+h) −f(x) h\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }limh→0​hf(x+h) −f(x) ​ for f(x) =2+6xf ( x ) = 2 + 6 xf(x) =2+6x .

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Determine any points on the graph of the following function at which the tangent line is horizontal. f(x) =x2+6x−8f ( x ) = x ^ { 2 } + 6 x - 8f(x) =x2+6x−8

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Use the limit process to find the slope of the graph of 6x−4x2 6 x-4 x^{2} 6x−4x2 at (7,−154) (7,-154) (7,−154) .

Correct AnswerverifiedShow Answer

Find an equation of the tangent line to the graph of the following function at the point $(-1,-5)$ $-3 x^{2}-2$

Correct Answer
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Correct Answer
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Correct Answer
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Find $\lim _ { x \rightarrow - \infty } \left[ \frac { x } { ( 7 + x ) ^ { 2 } } - 6 \right]$ (if it exists) .

Correct Answer
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Using the summation formulas and properties, evaluate the following expression. $\sum _ { i = 1 } ^ { 60 } 4$

Correct Answer
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Find the following limit, if it exists. $\lim _ { x \rightarrow - 3 } \frac { 9 - 3 x - 2 x ^ { 2 } } { 3 + x }$

Correct Answer
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Use the graph to find $\lim _ { x \rightarrow 3 } \frac { 4 x ^ { 2 } - 36 } { x - 3 }$ . $Use the graph to find \lim _ { x \rightarrow 3 } \frac { 4 x ^ { 2 } - 36 } { x - 3 } . A) 24 B) \infty C) 12 D) 0 E) limit does not exist$

Correct Answer
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Correct Answer
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Find $\lim _ { x \rightarrow 8 } \frac { 5 x } { \sqrt { x + 2 } }$ by direct substitution.

Correct Answer
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Use the figure below to approximate the slope of the curve at the point $( x , y )$ . $Use the figure below to approximate the slope of the curve at the point ( x , y ) . A) 2 B) \frac { 3 } { 2 } C) - 2 D) - 1 E) 1$

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Use the first six terms to predict the limit of the sequence $a _ { n } = \frac { 5 n ^ { 3 } + 8 } { n + 3 }$ (assume $n$ begins with 1 ) .

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Use the limit process to find the slope of the graph of $\sqrt { x + 4 }$ at $( 5,3 )$ .

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Find $\lim _ { x \rightarrow 6 } \frac { 4 x } { \sqrt { x + 4 } }$ by direct substitution.

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Use the function below and its derivative to determine any points on the graph of $f$ at which the tangent line is horizontal. $f(x) =3 x^{4}-6 x^{2}, \quad f^{\prime}(x) =12 x^{3}-12 x$

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Use asymptotes to match $f(x) =\frac{4 x^{2}}{x^{2}+1}$ with its graph.

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Find the following limit. $\lim _ { x \rightarrow - 4 } 3 x ^ { 2 } + 3 x + 1$

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Use the limit process to find the slope of the graph of $\sqrt{x+21}$ at $(4,5)$ .

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Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ for $f ( x ) = 2 + 6 x$ .

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Determine any points on the graph of the following function at which the tangent line is horizontal. $f ( x ) = x ^ { 2 } + 6 x - 8$

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Use the limit process to find the slope of the graph of $6 x-4 x^{2}$ at $(7,-154)$ .

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