Question 1

Match the function with the correct table values.
- f(x) =x2+5x+6x2+7x+12f ( x )  = \frac { x ^ { 2 } + 5 x + 6 } { x ^ { 2 } + 7 x + 12 }f(x) =x2+7x+12x2+5x+6​

Accepted Answer

A)    0.7101;0.7139;0.7142;0.7143;0.7147;0.71830.7101 ; 0.7139 ; 0.7142 ; 0.7143 ; 0.7147 ; 0.71830.7101;0.7139;0.7142;0.7143;0.7147;0.7183 
B)    −1.1222;−0.9202;−0.9020;−0.8980;−0.8802;−0.7182- 1.1222 ; - 0.9202 ; - 0.9020 ; - 0.8980 ; - 0.8802 ; - 0.7182−1.1222;−0.9202;−0.9020;−0.8980;−0.8802;−0.7182 
C)    −1.2222;−1.0202;−1.0020;−0.9980;−0.9802;−0.8182- 1.2222 ; - 1.0202 ; - 1.0020 ; - 0.9980 ; - 0.9802 ; - 0.8182−1.2222;−1.0202;−1.0020;−0.9980;−0.9802;−0.8182 
D)    −1.3222;−1.1202;−1.1020;−1.0980;−1.0802;−0.9182- 1.3222 ; - 1.1202 ; - 1.1020 ; - 1.0980 ; - 1.0802 ; - 0.9182−1.3222;−1.1202;−1.1020;−1.0980;−1.0802;−0.9182E) A) and C)
F) C) and D)

Question 2

Use NINT on a calculator to find the numerical integral of the function over the specified interval.
- f(x) =x36+x2;[0,10]f ( x )  = \frac { x } { 36 + x ^ { 2 } } ; [ 0,10 ]f(x) =36+x2x​;[0,10] 
Round to three decimal places.

Accepted Answer

A)    1.8991.8991.899 
B)    0.3320.3320.332 
C)    0.6650.6650.665 
D)    −0.665- 0.665−0.665E) B) and C)
F) All of the above

Question 3

Find the limit of the function by using direct substitution.
- lim⁡x→π/2(4excos⁡x) \lim _ { x \rightarrow \pi / 2 } \left( 4 e ^ { x } \cos x \right) limx→π/2​(4excosx)

Accepted Answer

A)   0
B)   1
C)    π2\frac { \pi } { 2 }2π​ 
D)    4eπ/24 \mathrm { e } ^ { \pi / 2 }4eπ/2E) All of the above
F) A) and B)

Question 4

Find the limit.
-Let  lim⁡x→7f(x) =−5\lim _ { x \rightarrow 7 } f ( x )  = - 5limx→7​f(x) =−5  and  lim⁡x→7g(x) =−10\lim _ { x \rightarrow 7 } g ( x )  = - 10limx→7​g(x) =−10 . Find  lim⁡x→7f(x) g(x) \lim _ { x \rightarrow 7 } \frac { f ( x )  } { g ( x )  }limx→7​g(x) f(x) ​ .

Accepted Answer

A)   5
B)   2
C)    12\frac { 1 } { 2 }21​ 
D)    −7- 7−7E) A) and D)
F) A) and C)

Question 5

Find the limit of the function algebraically.
- lim⁡x→3x2−2x−15x+3\lim _ { x \rightarrow 3 } \frac { x ^ { 2 } - 2 x - 15 } { x + 3 }limx→3​x+3x2−2x−15​

Accepted Answer

A)   Does not exist
B)    −8- 8−8 
C)   0
D)   5 E) A) and D)
F) A) and C)

Question 6

Find the indicated limit.
- lim⁡x→xcos⁡1x\lim _ { x \rightarrow } x \cos \frac { 1 } { x }limx→​xcosx1​

Accepted Answer

A)    ∝\propto∝ 
B)   0
C)    −∞- \infty−∞ 
D)   1 E) C) and D)
F) A) and B)

Question 7

Find the derivative of the function at the specified point.
- f(x) =5x+9f ( x )  = 5 x + 9f(x) =5x+9  at  x=2x = 2x=2

Accepted Answer

A)   0
B)   5
C)   10
D)   9 E) A) and D)
F) B) and C)

Question 8

Compute the average of the RRAM and LRAM approximations to estimate the area between the graph of the function
and the x-axis over the given interval using the indicated number of subintervals. (The function is non-negative on the
given interval) .
- f(x) =16+6x−x2;[0,4];4f ( x )  = 16 + 6 x - x ^ { 2 } ; [ 0,4 ] ; 4f(x) =16+6x−x2;[0,4];4  subintervals

Accepted Answer

A)    2254\frac { 225 } { 4 }4225​ 
B)   115
C)   230
D)    2252\frac { 225 } { 2 }2225​E) None of the above
F) A) and B)

Question 9

Solve the problem.
-A snail travels at  0.40.40.4  feet/min for 5 minutes. How far does it travel?

Accepted Answer

A)    0.4ft0.4 \mathrm { ft }0.4ft 
B)    5ft5 \mathrm { ft }5ft 
C)    2ft2 \mathrm { ft }2ft 
D)    0.45ft\frac { 0.4 } { 5 } \mathrm { ft }50.4​ftE) None of the above
F) C) and D)

Question 10

Solve the problem.
-The position of an object at time  ttt  is given by  s(t) s ( t ) s(t)  . Find the instantaneous velocity at the indicated value of  ttt .  s(t) =−7−5s ( t )  = - 7 - 5s(t) =−7−5  t at  t=4t = 4t=4

Accepted Answer

A)   5
B)    −27- 27−27 
C)    −5- 5−5 
D)    −7- 7−7E) C) and D)
F) B) and C)

Question 11

Find the equation of the tangent line to the curve when x has the given value.
- f(x) =x;x=25f ( x )  = \sqrt { x } ; x = 25f(x) =x​;x=25

Accepted Answer

A)    y=110x+4y = \frac { 1 } { 10 } x + 4y=101​x+4 
B)    y=−110x+52y = - \frac { 1 } { 10 } x + \frac { 5 } { 2 }y=−101​x+25​ 
C)    y=110x+52y = \frac { 1 } { 10 } x + \frac { 5 } { 2 }y=101​x+25​ 
D)    y=110x−52y = \frac { 1 } { 10 } x - \frac { 5 } { 2 }y=101​x−25​E) All of the above
F) A) and D)

Question 12

Find the derivative of the function using the definition of derivative.
- f(x) =−2xf ( x )  = - \frac { 2 } { x }f(x) =−x2​

Accepted Answer

A)    f′(x) =−2x2f ^ { \prime } ( x )  = - 2 x ^ { 2 }f′(x) =−2x2 
B)    f′(x) =−2x2f ^ { \prime } ( x )  = - \frac { 2 } { x ^ { 2 } }f′(x) =−x22​ 
C)    f′(x) =−2f ^ { \prime } ( x )  = - 2f′(x) =−2 
D)    f′(x) =2x2f ^ { \prime } ( x )  = \frac { 2 } { x ^ { 2 } }f′(x) =x22​E) None of the above
F) C) and D)

Question 13

Solve the problem.
-Estimate the "RRAM" area under the graph of the function above the  xxx -axis and under the graph of the function from  x=0x = 0x=0  to  x=5x = 5x=5 . Use 5 subintervals.

Accepted Answer

A)   15.5
B)   18.75
C)   17.5
D)   14.5 E) C) and D)
F) None of the above

Question 14

Find the derivative of the function at the specified point.
- g(x) =x3+5xg ( x )  = x ^ { 3 } + 5 xg(x) =x3+5x  at  x=1x = 1x=1

Accepted Answer

A)   8
B)   3
C)   7
D)   6 E) C) and D)
F) A) and C)

Question 15

Use graphs and tables to find the limit and identify any vertical asymptotes.
- lim⁡x→9−xx−9\lim _ { x \rightarrow 9 ^ { - } } \frac { x } { x - 9 }limx→9−​x−9x​

Accepted Answer

A)   9 ; no vertical asymptotes
B)    x;x=9x ; x = 9x;x=9 
C)    −∞;x=−9- \infty ; x = - 9−∞;x=−9 
D)    −∞;x=9- \infty ; x = 9−∞;x=9E) A) and C)
F) B) and D)

Question 16

Find the derivative of the function at the specified point.
- f(x) =8x+2f ( x )  = \frac { 8 } { x + 2 }f(x) =x+28​  at  x=0x = 0x=0

Accepted Answer

A)    −2- 2−2 
B)    −32- 32−32 
C)   8
D)   2 E) A) and C)
F) C) and D)

Question 17

Find the definite integral by computing an area.
- ∫057xdx\int _ { 0 } ^ { 5 } 7 x d x∫05​7xdx

Accepted Answer

A)   175
B)   35
C)    1752\frac { 175 } { 2 }2175​ 
D)    252\frac { 25 } { 2 }225​E) C) and D)
F) B) and D)

Question 18

Use NDER on a calculator to find the numerical derivative of the function at the specified point.
- f(x) =−4x2+7xf ( x )  = - 4 x ^ { 2 } + 7 xf(x) =−4x2+7x  at  x=5x = 5x=5

Accepted Answer

A)   3
B)    −33- 33−33 
C)    −13- 13−13 
D)   33 E) A) and D)
F) A) and B)

Question 19

Match the function with the correct table values.
- f(x) =x4−1x−1f ( x )  = \frac { x ^ { 4 } - 1 } { x - 1 }f(x) =x−1x4−1​

Accepted Answer

A)    4.595;5.046;5.095;5.105;5.154;5.6774.595 ; 5.046 ; 5.095 ; 5.105 ; 5.154 ; 5.6774.595;5.046;5.095;5.105;5.154;5.677 
B)    1.032;1.182;1.198;1.201;1.218;1.3921.032 ; 1.182 ; 1.198 ; 1.201 ; 1.218 ; 1.3921.032;1.182;1.198;1.201;1.218;1.392 
C)    3.439;3.940;3.994;4.006;4.060;4.6413.439 ; 3.940 ; 3.994 ; 4.006 ; 4.060 ; 4.6413.439;3.940;3.994;4.006;4.060;4.641D) All of the above
E) None of the above

Question 20

Solve the problem.
-A toy rocket is launched straight up from level ground. Its velocity function is  f(t) =189−32tft/sec\mathrm { f } ( \mathrm { t } )  = 189 - 32 \mathrm { t } \mathrm { ft } / \mathrm { sec }f(t) =189−32tft/sec , where  t\mathrm { t }t  is the number of seconds after launch. At what time does the rocket reach its maximum height?

Accepted Answer

A)    6.23sec6.23 \mathrm { sec }6.23sec 
B)    5.72sec5.72 \mathrm { sec }5.72sec 
C)    5.91sec5.91 \mathrm { sec }5.91sec 
D)    11.81sec11.81 \mathrm { sec }11.81secE) A) and B)
F) A) and C)

Exam 11: An Introduction to Calculus: Limits, Derivatives, and Integrals

Solve the problem. -A snail travels at $0.4$ feet/min for 5 minutes. How far does it travel?

Correct Answer
verified

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - $f ( x ) = \frac { x } { 36 + x ^ { 2 } } ; [ 0,10 ]$ Round to three decimal places.

Correct Answer
verified

Use graphs and tables to find the limit and identify any vertical asymptotes. - $\lim _ { x \rightarrow 9 ^ { - } } \frac { x } { x - 9 }$

Correct Answer
verified

Correct Answer
verified

Find the derivative of the function at the specified point. - $f ( x ) = 5 x + 9$ at $x = 2$

Correct Answer
verified

Solve the problem. -The position of an object at time $t$ is given by $s ( t )$ . Find the instantaneous velocity at the indicated value of $t$ . $s ( t ) = - 7 - 5$ t at $t = 4$

Correct Answer
verified

Find the limit. -Let $\lim _ { x \rightarrow 7 } f ( x ) = - 5$ and $\lim _ { x \rightarrow 7 } g ( x ) = - 10$ . Find $\lim _ { x \rightarrow 7 } \frac { f ( x ) } { g ( x ) }$ .

Correct Answer
verified

Find the indicated limit. - $\lim _ { x \rightarrow } x \cos \frac { 1 } { x }$

Correct Answer
verified

Find the definite integral by computing an area. - $\int _ { 0 } ^ { 5 } 7 x d x$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Find the derivative of the function at the specified point. - $f ( x ) = \frac { 8 } { x + 2 }$ at $x = 0$

Correct Answer
verified

Solve the problem. -Estimate the "RRAM" area under the graph of the function above the $x$ -axis and under the graph of the function from $x = 0$ to $x = 5$ . Use 5 subintervals.

Correct Answer
verified

Find the derivative of the function at the specified point. - $g ( x ) = x ^ { 3 } + 5 x$ at $x = 1$

Correct Answer
verified

Correct Answer
verified

Find the limit of the function by using direct substitution. - $\lim _ { x \rightarrow \pi / 2 } \left( 4 e ^ { x } \cos x \right)$

Correct Answer
verified

Find the derivative of the function using the definition of derivative. - $f ( x ) = - \frac { 2 } { x }$

Correct Answer
verified

Find the equation of the tangent line to the curve when x has the given value. - $f ( x ) = \sqrt { x } ; x = 25$

Correct Answer
verified

Use NDER on a calculator to find the numerical derivative of the function at the specified point. - $f ( x ) = - 4 x ^ { 2 } + 7 x$ at $x = 5$

Correct Answer
verified

Find the limit of the function algebraically. - $\lim _ { x \rightarrow 3 } \frac { x ^ { 2 } - 2 x - 15 } { x + 3 }$

Correct Answer
verified

Exam 11: An Introduction to Calculus: Limits, Derivatives, and Integrals

Solve the problem. -A snail travels at 0.40.40.4 feet/min for 5 minutes. How far does it travel?

Correct AnswerverifiedShow Answer

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - f(x) =x36+x2;[0,10]f ( x ) = \frac { x } { 36 + x ^ { 2 } } ; [ 0,10 ]f(x) =36+x2x​;[0,10] Round to three decimal places.

Correct AnswerverifiedShow Answer

Use graphs and tables to find the limit and identify any vertical asymptotes. - lim⁡x→9−xx−9\lim _ { x \rightarrow 9 ^ { - } } \frac { x } { x - 9 }limx→9−​x−9x​

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the derivative of the function at the specified point. - f(x) =5x+9f ( x ) = 5 x + 9f(x) =5x+9 at x=2x = 2x=2

Correct AnswerverifiedShow Answer

Solve the problem. -The position of an object at time ttt is given by s(t) s ( t ) s(t) . Find the instantaneous velocity at the indicated value of ttt . s(t) =−7−5s ( t ) = - 7 - 5s(t) =−7−5 t at t=4t = 4t=4

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the indicated limit. - lim⁡x→xcos⁡1x\lim _ { x \rightarrow } x \cos \frac { 1 } { x }limx→​xcosx1​

Correct AnswerverifiedShow Answer

Find the definite integral by computing an area. - ∫057xdx\int _ { 0 } ^ { 5 } 7 x d x∫05​7xdx

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Match the function with the correct table values. - f(x) =x4−1x−1f ( x ) = \frac { x ^ { 4 } - 1 } { x - 1 }f(x) =x−1x4−1​

Correct AnswerverifiedShow Answer

Find the derivative of the function at the specified point. - f(x) =8x+2f ( x ) = \frac { 8 } { x + 2 }f(x) =x+28​ at x=0x = 0x=0

Correct AnswerverifiedShow Answer

Solve the problem. -Estimate the "RRAM" area under the graph of the function above the xxx -axis and under the graph of the function from x=0x = 0x=0 to x=5x = 5x=5 . Use 5 subintervals.

Correct AnswerverifiedShow Answer

Find the derivative of the function at the specified point. - g(x) =x3+5xg ( x ) = x ^ { 3 } + 5 xg(x) =x3+5x at x=1x = 1x=1

Correct AnswerverifiedShow Answer

Match the function with the correct table values. - f(x) =x2+5x+6x2+7x+12f ( x ) = \frac { x ^ { 2 } + 5 x + 6 } { x ^ { 2 } + 7 x + 12 }f(x) =x2+7x+12x2+5x+6​

Correct AnswerverifiedShow Answer

Find the limit of the function by using direct substitution. - lim⁡x→π/2(4excos⁡x) \lim _ { x \rightarrow \pi / 2 } \left( 4 e ^ { x } \cos x \right) limx→π/2​(4excosx)

Correct AnswerverifiedShow Answer

Find the derivative of the function using the definition of derivative. - f(x) =−2xf ( x ) = - \frac { 2 } { x }f(x) =−x2​

Correct AnswerverifiedShow Answer

Find the equation of the tangent line to the curve when x has the given value. - f(x) =x;x=25f ( x ) = \sqrt { x } ; x = 25f(x) =x​;x=25

Correct AnswerverifiedShow Answer

Use NDER on a calculator to find the numerical derivative of the function at the specified point. - f(x) =−4x2+7xf ( x ) = - 4 x ^ { 2 } + 7 xf(x) =−4x2+7x at x=5x = 5x=5

Correct AnswerverifiedShow Answer

Find the limit of the function algebraically. - lim⁡x→3x2−2x−15x+3\lim _ { x \rightarrow 3 } \frac { x ^ { 2 } - 2 x - 15 } { x + 3 }limx→3​x+3x2−2x−15​

Correct AnswerverifiedShow Answer

Solve the problem. -A snail travels at $0.4$ feet/min for 5 minutes. How far does it travel?

Correct Answer
verified

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - $f ( x ) = \frac { x } { 36 + x ^ { 2 } } ; [ 0,10 ]$ Round to three decimal places.

Correct Answer
verified

Use graphs and tables to find the limit and identify any vertical asymptotes. - $\lim _ { x \rightarrow 9 ^ { - } } \frac { x } { x - 9 }$

Correct Answer
verified

Correct Answer
verified

Find the derivative of the function at the specified point. - $f ( x ) = 5 x + 9$ at $x = 2$

Correct Answer
verified

Solve the problem. -The position of an object at time $t$ is given by $s ( t )$ . Find the instantaneous velocity at the indicated value of $t$ . $s ( t ) = - 7 - 5$ t at $t = 4$

Correct Answer
verified

Correct Answer
verified

Find the indicated limit. - $\lim _ { x \rightarrow } x \cos \frac { 1 } { x }$

Correct Answer
verified

Find the definite integral by computing an area. - $\int _ { 0 } ^ { 5 } 7 x d x$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Find the derivative of the function at the specified point. - $f ( x ) = \frac { 8 } { x + 2 }$ at $x = 0$

Correct Answer
verified

Solve the problem. -Estimate the "RRAM" area under the graph of the function above the $x$ -axis and under the graph of the function from $x = 0$ to $x = 5$ . Use 5 subintervals.

Correct Answer
verified

Find the derivative of the function at the specified point. - $g ( x ) = x ^ { 3 } + 5 x$ at $x = 1$

Correct Answer
verified

Correct Answer
verified

Find the limit of the function by using direct substitution. - $\lim _ { x \rightarrow \pi / 2 } \left( 4 e ^ { x } \cos x \right)$

Correct Answer
verified

Find the derivative of the function using the definition of derivative. - $f ( x ) = - \frac { 2 } { x }$

Correct Answer
verified

Find the equation of the tangent line to the curve when x has the given value. - $f ( x ) = \sqrt { x } ; x = 25$

Correct Answer
verified

Use NDER on a calculator to find the numerical derivative of the function at the specified point. - $f ( x ) = - 4 x ^ { 2 } + 7 x$ at $x = 5$

Correct Answer
verified

Find the limit of the function algebraically. - $\lim _ { x \rightarrow 3 } \frac { x ^ { 2 } - 2 x - 15 } { x + 3 }$

Correct Answer
verified