Exam 13: A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Explore all topics

Solve the problem. -If an object is thrown straight upward from the ground with an initial speed of 112 feet per second, then its height, h, in feet after t seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 112 t$ Find the instantaneous speed of the Object at t = 6.

(Multiple Choice)

4.9/5

(36)

Question 141

Use the graph shown to determine if the limit exists. If it does, find its value. - $\lim _ { x \rightarrow 4 } f ( x )$ $Use the graph shown to determine if the limit exists. If it does, find its value. - \lim _ { x \rightarrow 4 } f ( x )$

(Multiple Choice)

4.7/5

(29)

Question 142

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

(Multiple Choice)

5.0/5

(39)

Question 143

Find the numbers at which f is continuous. At which numbers is f discontinuous? - $f ( x ) = \left\{ \begin{array} { r r } \frac { x ^ { 2 } - 16 } { x - 4 } & \text { if } x \neq 4 \\8 & \text { if } x = 4\end{array} \right.$

(Multiple Choice)

4.9/5

(33)

Question 144

Determine whether f is continuous at c. - $f ( x ) = \frac { 5 } { x + 2 } ; c = - 2$

(Multiple Choice)

4.8/5

(36)

Question 145

Showing 141 - 145 of 145

Solve the problem. -If an object is thrown straight upward from the ground with an initial speed of 112 feet per second, then its height, h, in feet after t seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 112 t$ Find the instantaneous speed of the Object at t = 6.

Use the graph shown to determine if the limit exists. If it does, find its value. - $\lim _ { x \rightarrow 4 } f ( x )$ $Use the graph shown to determine if the limit exists. If it does, find its value. - \lim _ { x \rightarrow 4 } f ( x )$

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

Find the numbers at which f is continuous. At which numbers is f discontinuous? - $f ( x ) = \left\{ \begin{array} { r r } \frac { x ^ { 2 } - 16 } { x - 4 } & \text { if } x \neq 4 \\8 & \text { if } x = 4\end{array} \right.$

Determine whether f is continuous at c. - $f ( x ) = \frac { 5 } { x + 2 } ; c = - 2$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Review

Filters

Exam 13: A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Use the graph shown to determine if the limit exists. If it does, find its value. - lim⁡x→4f(x)\lim _ { x \rightarrow 4 } f ( x )limx→4​f(x)

Find the limit 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​

Determine whether f is continuous at c. - f(x)=5x+2;c=−2f ( x ) = \frac { 5 } { x + 2 } ; c = - 2f(x)=x+25​;c=−2

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Review

Filters

Use the graph shown to determine if the limit exists. If it does, find its value. - $\lim _ { x \rightarrow 4 } f ( x )$ $Use the graph shown to determine if the limit exists. If it does, find its value. - \lim _ { x \rightarrow 4 } f ( x )$

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

Determine whether f is continuous at c. - $f ( x ) = \frac { 5 } { x + 2 } ; c = - 2$