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

Match the function with the correct table values. - $f ( x ) = \frac { x - 4 } { \sqrt { x } - 2 }$ $Match the function with the correct table values. - f ( x ) = \frac { x - 4 } { \sqrt { x } - 2 }$

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

B

Match the function with the correct table values. - $f ( x ) = x ^ { 2 } - 5$ $Match the function with the correct table values. - f ( x ) = x ^ { 2 } - 5$

Free

(Multiple Choice)

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Question 2

Correct Answer:

Verified

A

Find the derivative of the function using the definition of derivative. - $f ( x ) = \sqrt { x + 4 }$

Free

(Multiple Choice)

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Question 3

Correct Answer:

Verified

B

Find the limit of the function by using direct substitution. - $\lim _ { x \rightarrow 2 } \left( x ^ { 2 } + 8 x - 2 \right)$

(Multiple Choice)

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Question 4

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - $f ( x ) = 2 x ^ { 2 } + 6 x + 4 ; [ - 3,3 ]$

(Multiple Choice)

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Question 5

Estimate the slope of the tangent line at the indicated point. -

(Multiple Choice)

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Question 6

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 $t$ . $s ( t ) = 3 t ^ { 2 } + 5 t + 7$ at $t = 4$

(Multiple Choice)

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Question 7

Estimate the slope of the tangent line at the indicated point. -

(Multiple Choice)

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Question 8

Find the indicated limit, if it exists. - $\lim _ { x \rightarrow 0 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } 4 x - 7 & x < 0 \\| 3 - x | & x \geq 0\end{array} \right.$

(Multiple Choice)

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Question 9

Use the given graph to determine the limit, if it exists. -

(Multiple Choice)

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Question 10

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.

(Multiple Choice)

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Question 11

Find the definite integral by computing an area. - $\int _ { 2 } ^ { 6 } x d x$

(Multiple Choice)

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Question 12

Find the indicated limit. - $\lim _ { x \rightarrow 0 } \frac { \tan ^ { 2 } ( x ) } { x }$

(Multiple Choice)

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Question 13

Use a graph of the function to find the derivative of the function at the given point, if it exists. - $f ( x ) = \left\{ \begin{array} { l l } 7 + x & x \leq 2 \\ - x - 4 & x > 2 \end{array} \quad \right.$ at $x = 2$

(Multiple Choice)

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(28)

Question 14

Find the limit of the function algebraically. - $\lim _ { x \rightarrow 10 } \frac { x ^ { 2 } - 100 } { x - 10 }$

(Multiple Choice)

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(36)

Question 15

Determine the limit algebraically, if possible. - $\lim _ { x \rightarrow 0 } \frac { 9 \tan x } { 4 x }$

(Multiple Choice)

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(37)

Question 16

Find the indicated limit, if it exists. - $\lim _ { x \rightarrow 4 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } x + 1 & x < 4 \\1 - x & x \geq 4\end{array} \right.$

(Multiple Choice)

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Question 17

Find the limit of the function by using direct substitution. - $\lim _ { x \rightarrow 2 \pi } \ln ( \cos x )$

(Multiple Choice)

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Question 18

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - $f ( x ) = x ^ { 5 } ; [ 0,1 ]$

(Multiple Choice)

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Question 19

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - $f ( x ) = \frac { 1 } { 1 + 9 x } ; [ 0,9 ]$ Round to three decimal places.

(Multiple Choice)

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Question 20

Match the function with the correct table values. - $f ( x ) = \frac { x - 4 } { \sqrt { x } - 2 }$ $Match the function with the correct table values. - f ( x ) = \frac { x - 4 } { \sqrt { x } - 2 }$

Match the function with the correct table values. - $f ( x ) = x ^ { 2 } - 5$ $Match the function with the correct table values. - f ( x ) = x ^ { 2 } - 5$

Find the derivative of the function using the definition of derivative. - $f ( x ) = \sqrt { x + 4 }$

Find the limit of the function by using direct substitution. - $\lim _ { x \rightarrow 2 } \left( x ^ { 2 } + 8 x - 2 \right)$

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - $f ( x ) = 2 x ^ { 2 } + 6 x + 4 ; [ - 3,3 ]$

Estimate the slope of the tangent line at the indicated point. -

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 $t$ . $s ( t ) = 3 t ^ { 2 } + 5 t + 7$ at $t = 4$

Estimate the slope of the tangent line at the indicated point. -

Find the indicated limit, if it exists. - $\lim _ { x \rightarrow 0 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } 4 x - 7 & x < 0 \\| 3 - x | & x \geq 0\end{array} \right.$

Use the given graph to determine the limit, if it exists. -

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.

Find the definite integral by computing an area. - $\int _ { 2 } ^ { 6 } x d x$

Find the indicated limit. - $\lim _ { x \rightarrow 0 } \frac { \tan ^ { 2 } ( x ) } { x }$

Use a graph of the function to find the derivative of the function at the given point, if it exists. - $f ( x ) = \left\{ \begin{array} { l l } 7 + x & x \leq 2 \\ - x - 4 & x > 2 \end{array} \quad \right.$ at $x = 2$

Find the limit of the function algebraically. - $\lim _ { x \rightarrow 10 } \frac { x ^ { 2 } - 100 } { x - 10 }$

Determine the limit algebraically, if possible. - $\lim _ { x \rightarrow 0 } \frac { 9 \tan x } { 4 x }$

Find the indicated limit, if it exists. - $\lim _ { x \rightarrow 4 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } x + 1 & x < 4 \\1 - x & x \geq 4\end{array} \right.$

Find the limit of the function by using direct substitution. - $\lim _ { x \rightarrow 2 \pi } \ln ( \cos x )$

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - $f ( x ) = x ^ { 5 } ; [ 0,1 ]$

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - $f ( x ) = \frac { 1 } { 1 + 9 x } ; [ 0,9 ]$ Round to three decimal places.

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

Prerequisites

Filters

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

Match the function with the correct table values. - f(x)=x−4x−2f ( x ) = \frac { x - 4 } { \sqrt { x } - 2 }f(x)=x​−2x−4​

Match the function with the correct table values. - f(x)=x2−5f ( x ) = x ^ { 2 } - 5f(x)=x2−5

Find the derivative of the function using the definition of derivative. - f(x)=x+4f ( x ) = \sqrt { x + 4 }f(x)=x+4​

Find the limit of the function by using direct substitution. - lim⁡x→2(x2+8x−2)\lim _ { x \rightarrow 2 } \left( x ^ { 2 } + 8 x - 2 \right)limx→2​(x2+8x−2)

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - f(x)=2x2+6x+4;[−3,3]f ( x ) = 2 x ^ { 2 } + 6 x + 4 ; [ - 3,3 ]f(x)=2x2+6x+4;[−3,3]

Estimate the slope of the tangent line at the indicated point. -

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)=3t2+5t+7s ( t ) = 3 t ^ { 2 } + 5 t + 7s(t)=3t2+5t+7 at t=4t = 4t=4

Estimate the slope of the tangent line at the indicated point. -

Find the indicated limit, if it exists. - lim⁡x→0f(x),f(x)={4x−7x<0∣3−x∣x≥0\lim _ { x \rightarrow 0 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } 4 x - 7 & x < 0 \\| 3 - x | & x \geq 0\end{array} \right.limx→0​f(x),f(x)={4x−7∣3−x∣​x<0x≥0​

Use the given graph to determine the limit, if it exists. -

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.

Find the definite integral by computing an area. - ∫26xdx\int _ { 2 } ^ { 6 } x d x∫26​xdx

Find the indicated limit. - lim⁡x→0tan⁡2(x)x\lim _ { x \rightarrow 0 } \frac { \tan ^ { 2 } ( x ) } { x }limx→0​xtan2(x)​

Use a graph of the function to find the derivative of the function at the given point, if it exists. - f(x)={7+xx≤2−x−4x>2f ( x ) = \left\{ \begin{array} { l l } 7 + x & x \leq 2 \\ - x - 4 & x > 2 \end{array} \quad \right.f(x)={7+x−x−4​x≤2x>2​ at x=2x = 2x=2

Find the limit of the function algebraically. - lim⁡x→10x2−100x−10\lim _ { x \rightarrow 10 } \frac { x ^ { 2 } - 100 } { x - 10 }limx→10​x−10x2−100​

Determine the limit algebraically, if possible. - lim⁡x→09tan⁡x4x\lim _ { x \rightarrow 0 } \frac { 9 \tan x } { 4 x }limx→0​4x9tanx​

Find the indicated limit, if it exists. - lim⁡x→4f(x),f(x)={x+1x<41−xx≥4\lim _ { x \rightarrow 4 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } x + 1 & x < 4 \\1 - x & x \geq 4\end{array} \right.limx→4​f(x),f(x)={x+11−x​x<4x≥4​

Find the limit of the function by using direct substitution. - lim⁡x→2πln⁡(cos⁡x)\lim _ { x \rightarrow 2 \pi } \ln ( \cos x )limx→2π​ln(cosx)

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - f(x)=x5;[0,1]f ( x ) = x ^ { 5 } ; [ 0,1 ]f(x)=x5;[0,1]

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - f(x)=11+9x;[0,9]f ( x ) = \frac { 1 } { 1 + 9 x } ; [ 0,9 ]f(x)=1+9x1​;[0,9] Round to three decimal places.

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

Prerequisites

Filters

Match the function with the correct table values. - $f ( x ) = \frac { x - 4 } { \sqrt { x } - 2 }$ $Match the function with the correct table values. - f ( x ) = \frac { x - 4 } { \sqrt { x } - 2 }$

Match the function with the correct table values. - $f ( x ) = x ^ { 2 } - 5$ $Match the function with the correct table values. - f ( x ) = x ^ { 2 } - 5$

Find the derivative of the function using the definition of derivative. - $f ( x ) = \sqrt { x + 4 }$

Find the limit of the function by using direct substitution. - $\lim _ { x \rightarrow 2 } \left( x ^ { 2 } + 8 x - 2 \right)$

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - $f ( x ) = 2 x ^ { 2 } + 6 x + 4 ; [ - 3,3 ]$

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 $t$ . $s ( t ) = 3 t ^ { 2 } + 5 t + 7$ at $t = 4$

Find the indicated limit, if it exists. - $\lim _ { x \rightarrow 0 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } 4 x - 7 & x < 0 \\| 3 - x | & x \geq 0\end{array} \right.$

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.

Find the definite integral by computing an area. - $\int _ { 2 } ^ { 6 } x d x$

Find the indicated limit. - $\lim _ { x \rightarrow 0 } \frac { \tan ^ { 2 } ( x ) } { x }$

Use a graph of the function to find the derivative of the function at the given point, if it exists. - $f ( x ) = \left\{ \begin{array} { l l } 7 + x & x \leq 2 \\ - x - 4 & x > 2 \end{array} \quad \right.$ at $x = 2$

Find the limit of the function algebraically. - $\lim _ { x \rightarrow 10 } \frac { x ^ { 2 } - 100 } { x - 10 }$

Determine the limit algebraically, if possible. - $\lim _ { x \rightarrow 0 } \frac { 9 \tan x } { 4 x }$

Find the indicated limit, if it exists. - $\lim _ { x \rightarrow 4 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } x + 1 & x < 4 \\1 - x & x \geq 4\end{array} \right.$

Find the limit of the function by using direct substitution. - $\lim _ { x \rightarrow 2 \pi } \ln ( \cos x )$

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - $f ( x ) = x ^ { 5 } ; [ 0,1 ]$

Use NINT on a calculator to find the numerical integral of the function over the specified interval. - $f ( x ) = \frac { 1 } { 1 + 9 x } ; [ 0,9 ]$ Round to three decimal places.