Question 1

Let $f ( x ) = 2 x ^ { 3 } - 15 x ^ { 2 } - 36 x - 2$ Then ƒ has a relative minimum at x =

Accepted Answer

A) 2 
B) 4 
C) 6 
D) 8 
E) 10 
A) 2 
B) 4 
C) 6 
D) 8 
E) 10

Question 2

Let $f ( x ) = x + 2 + \frac { 3 } { x - 1 }$ on $[ 2,7 ]$ Then the set of all c in (2,7) guaranteed by the Mean Value Theorem is

Accepted Answer

A)  $\{ 1 - \sqrt { 6 } \}$ 
B)  $\{ 1 + \sqrt { 6 } \}$ 
C)  $\{ 0 \}$ 
D)  $\{ 1 - \sqrt { 6 } , 1 + \sqrt { 6 } \}$ 
E)  $\{ 1 - \sqrt { 3 } , 0,1 + \sqrt { 3 } \}$ 
A)  $\{ 1 - \sqrt { 6 } \}$ 
B)  $\{ 1 + \sqrt { 6 } \}$ 
C)  $\{ 0 \}$ 
D)  $\{ 1 - \sqrt { 6 } , 1 + \sqrt { 6 } \}$ 
E)  $\{ 1 - \sqrt { 3 } , 0,1 + \sqrt { 3 } \}$

Question 3

The antiderivative of $f ( x ) = \frac { 1 } { 1 + x ^ { 2 } } + \frac { 2 } { x }$ is

Accepted Answer

A)  $- \tan ^ { - 1 } x + 2 \ln x + C$ 
B)  $\tan ^ { - 1 } x - 2 \ln x + C$ 
C)  $\tan ^ { - 1 } x + 2 \ln x + C$ 
D)  $- \tan ^ { - 1 } x - 2 \ln x + C$ 
E)  $\tan ^ { - 1 } x + \frac { 1 } { 2 } \ln x + C$ 
A)  $- \tan ^ { - 1 } x + 2 \ln x + C$ 
B)  $\tan ^ { - 1 } x - 2 \ln x + C$ 
C)  $\tan ^ { - 1 } x + 2 \ln x + C$ 
D)  $- \tan ^ { - 1 } x - 2 \ln x + C$ 
E)  $\tan ^ { - 1 } x + \frac { 1 } { 2 } \ln x + C$

Question 4

A post office regulation is that the sum of the length and girth of a parcel must not exceed 6 feet. The largest volume in cubic feet of a parcel with square ends is
​

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
E) 5 
A) 1 
B) 2 
C) 3 
D) 4 
E) 5

Question 5

Let $f ( x ) = \sin x + \cos x$ on $[ 0,2 \pi ]$ Then the set of all in c guaranteed by Rolle's Theorem is

Accepted Answer

A)  $\left\{ \frac { 3 \pi } { 4 } \right\}$ 
B)  $\left\{ \frac { 7 \pi } { 4 } \right\}$ 
C)  $\left\{ \frac { \pi } { 4 } , \frac { 5 \pi } { 4 } \right\}$ 
D)  $\left\{ \frac { \pi } { 4 } , \frac { 7 \pi } { 4 } \right\}$ 
E)  $\left\{ \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } \right\}$ 
A)  $\left\{ \frac { 3 \pi } { 4 } \right\}$ 
B)  $\left\{ \frac { 7 \pi } { 4 } \right\}$ 
C)  $\left\{ \frac { \pi } { 4 } , \frac { 5 \pi } { 4 } \right\}$ 
D)  $\left\{ \frac { \pi } { 4 } , \frac { 7 \pi } { 4 } \right\}$ 
E)  $\left\{ \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } \right\}$

Question 6

Let $f ( x ) = \ln x$ on $[ 1 , e ]$ Then the set of all c in (1,e) guaranteed by the Mean Value Theorem is

Accepted Answer

A)  $\{ 1.5 \}$ 
B)  $\{ e - 1 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ 2.5 \}$ 
E)  $\{ 1.5 , e - 1 \}$ 
A)  $\{ 1.5 \}$ 
B)  $\{ e - 1 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ 2.5 \}$ 
E)  $\{ 1.5 , e - 1 \}$

Question 7

The particular solution of the differential equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } = 12 x ^ { 2 }$ satisfying the boundary conditions when x = 0, y = 1 and x = 3, y' = 8 is

Accepted Answer

A)  $y = x ^ { 4 } - \frac { 8 } { 3 } x + 1$ 
B)  $y = x ^ { 4 } - \frac { 1 } { 3 } x + 1$ 
C)  $y = x ^ { 4 } - \frac { 74 } { 3 } x + 1$ 
D)  $y = x ^ { 4 } + \frac { 8 } { 3 } x + 1$ 
E)  $y = x ^ { 4 } + \frac { 74 } { 3 } x + 1$ 
A)  $y = x ^ { 4 } - \frac { 8 } { 3 } x + 1$ 
B)  $y = x ^ { 4 } - \frac { 1 } { 3 } x + 1$ 
C)  $y = x ^ { 4 } - \frac { 74 } { 3 } x + 1$ 
D)  $y = x ^ { 4 } + \frac { 8 } { 3 } x + 1$ 
E)  $y = x ^ { 4 } + \frac { 74 } { 3 } x + 1$

Question 8

The particular solution of the differential equation $\frac { d ^ { 2 } s } { d t ^ { 2 } } = 8 t - 3$ satisfying the initial conditions $\left. \frac { d s } { d t } \right| _ { x = 0 } = 4$ and $s ( 0 ) = 1$ is

Accepted Answer

A)  $s = \frac { 4 } { 3 } t ^ { 3 } - \frac { 3 } { 2 } t ^ { 2 } + 4 t + 1$ 
B)  $s = \frac { 4 } { 3 } t ^ { 3 } + \frac { 3 } { 2 } t ^ { 2 } - 4 t + 1$ 
C)  $s = \frac { 4 } { 3 } t ^ { 3 } - \frac { 3 } { 2 } t ^ { 2 } - 4 t + 1$ 
D)  $s = \frac { 4 } { 3 } t ^ { 3 } - \frac { 3 } { 2 } t ^ { 2 } + 4 t - 1$ 
E)  $s = \frac { 4 } { 3 } t ^ { 3 } + \frac { 3 } { 2 } t ^ { 2 } + 4 t + 1$ 
A)  $s = \frac { 4 } { 3 } t ^ { 3 } - \frac { 3 } { 2 } t ^ { 2 } + 4 t + 1$ 
B)  $s = \frac { 4 } { 3 } t ^ { 3 } + \frac { 3 } { 2 } t ^ { 2 } - 4 t + 1$ 
C)  $s = \frac { 4 } { 3 } t ^ { 3 } - \frac { 3 } { 2 } t ^ { 2 } - 4 t + 1$ 
D)  $s = \frac { 4 } { 3 } t ^ { 3 } - \frac { 3 } { 2 } t ^ { 2 } + 4 t - 1$ 
E)  $s = \frac { 4 } { 3 } t ^ { 3 } + \frac { 3 } { 2 } t ^ { 2 } + 4 t + 1$

Question 9

The antiderivative of $f ( x ) = \frac { 3 x ^ { 2 } - 5 x + 7 } { 2 x }$ is

Accepted Answer

A)  $\frac { 3 } { 4 } x ^ { 2 } - \frac { 5 } { 2 } x - \frac { 7 } { 2 } \ln x + C$ 
B)  $\frac { 3 } { 4 } x ^ { 2 } - \frac { 5 } { 2 } x + \frac { 7 } { 2 } \ln x + C$ 
C)  $\frac { 3 } { 4 } x ^ { 2 } + \frac { 5 } { 2 } x + \frac { 7 } { 2 } \ln x + C$ 
D)  $- \frac { 3 } { 4 } x ^ { 2 } - \frac { 5 } { 2 } x + \frac { 7 } { 2 } \ln x + C$ 
E)  $\frac { 3 } { 4 } x ^ { 2 } + \frac { 5 } { 2 } x - \frac { 7 } { 2 } \ln x + C$ 
A)  $\frac { 3 } { 4 } x ^ { 2 } - \frac { 5 } { 2 } x - \frac { 7 } { 2 } \ln x + C$ 
B)  $\frac { 3 } { 4 } x ^ { 2 } - \frac { 5 } { 2 } x + \frac { 7 } { 2 } \ln x + C$ 
C)  $\frac { 3 } { 4 } x ^ { 2 } + \frac { 5 } { 2 } x + \frac { 7 } { 2 } \ln x + C$ 
D)  $- \frac { 3 } { 4 } x ^ { 2 } - \frac { 5 } { 2 } x + \frac { 7 } { 2 } \ln x + C$ 
E)  $\frac { 3 } { 4 } x ^ { 2 } + \frac { 5 } { 2 } x - \frac { 7 } { 2 } \ln x + C$

Question 10

The smallest perimeter possible for a rectangle whose area is 400 square feet is
​

Accepted Answer

A) 79.5 ft 
B) 79.9 ft 
C) 80 ft 
D) 80.1 ft 
E) 80.5 ft 
A) 79.5 ft 
B) 79.9 ft 
C) 80 ft 
D) 80.1 ft 
E) 80.5 ft

Question 11

The largest set on which the function $f ( x ) = 3 \sin x$ on $[ 0,2 \pi ]$ is increasing is

Accepted Answer

A)  $\left( 0 , \frac { \pi } { 2 } \right)$ 
B)  $\left( \frac { \pi } { 2 } , \pi \right)$ 
C)  $\left( \pi , \frac { 3 \pi } { 2 } \right)$ 
D)  $\left( 0 , \frac { \pi } { 2 } \right) \cup \left( \frac { 3 \pi } { 2 } , 2 \pi \right)$ 
E)  $( 0,2 \pi )$ 
A)  $\left( 0 , \frac { \pi } { 2 } \right)$ 
B)  $\left( \frac { \pi } { 2 } , \pi \right)$ 
C)  $\left( \pi , \frac { 3 \pi } { 2 } \right)$ 
D)  $\left( 0 , \frac { \pi } { 2 } \right) \cup \left( \frac { 3 \pi } { 2 } , 2 \pi \right)$ 
E)  $( 0,2 \pi )$

Question 12

The maximum area of a rectangular piece of land that can be enclosed by 100 yards of fencing is
​

Accepted Answer

A) 578 yd2 
B) 625 yd2 
C) 676 yd2 
D) 576 yd2 
E) 748 yd2 
A) 578 yd2 
B) 625 yd2 
C) 676 yd2 
D) 576 yd2 
E) 748 yd2

Question 13

Determine which of the following is not true for the graph of $f ( x ) = \frac { 2 x ^ { 2 } + x - 1 } { x ^ { 2 } - 1 }$

Accepted Answer

A) ƒ has no relative maximum. 
B) ƒ has no relative minimum. 
C) ƒ has a vertical asymptote: x = 1. 
D) ƒ has a horizontal asymptote: y = 2. 
E) ƒ is concave downward on $( 1 , \infty ) .$ 
A) ƒ has no relative maximum. 
B) ƒ has no relative minimum. 
C) ƒ has a vertical asymptote: x = 1. 
D) ƒ has a horizontal asymptote: y = 2. 
E) ƒ is concave downward on $( 1 , \infty ) .$

Question 14

Let $f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } - 9 x + 1$ Then ƒ has a relative minimum at x =

Accepted Answer

A) -3 
B) -2 
C) -1 
D) 0 
E) 2 
A) -3 
B) -2 
C) -1 
D) 0 
E) 2

Question 15

The antiderivative of $f ( x ) = x ^ { 4 } + x - 3$ is

Accepted Answer

A)  $- \frac { x ^ { 5 } } { 5 } + \frac { x ^ { 2 } } { 2 } + 3 x + C$ 
B)  $4 x ^ { 3 } + 1$ 
C)  $\frac { x ^ { 5 } } { 5 } + \frac { x ^ { 2 } } { 2 } + 3 x + C$ 
D)  $\frac { x ^ { 5 } } { 5 } + \frac { x ^ { 2 } } { 2 } - 3 x + C$ 
E)  $- \frac { x ^ { 5 } } { 5 } + \frac { x ^ { 2 } } { 2 } - 3 x + C$ 
A)  $- \frac { x ^ { 5 } } { 5 } + \frac { x ^ { 2 } } { 2 } + 3 x + C$ 
B)  $4 x ^ { 3 } + 1$ 
C)  $\frac { x ^ { 5 } } { 5 } + \frac { x ^ { 2 } } { 2 } + 3 x + C$ 
D)  $\frac { x ^ { 5 } } { 5 } + \frac { x ^ { 2 } } { 2 } - 3 x + C$ 
E)  $- \frac { x ^ { 5 } } { 5 } + \frac { x ^ { 2 } } { 2 } - 3 x + C$

Question 16

Let $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 15 x$ Then ƒ has a relative minimum at x =

Accepted Answer

A) 0 
B) 1 
C) 2 
D) 4 
E) 5 
A) 0 
B) 1 
C) 2 
D) 4 
E) 5

Question 17

The particular solution of the differential equation $\frac { d ^ { 2 } s } { d t ^ { 2 } } = - 9.8$ satisfying the initial conditions $\left[ \frac { d s } { d t } ( 0 ) \right] = 160$ and $s ( 0 ) = 3$ is

Accepted Answer

A)  $s = - 4.9 t ^ { 2 } + 160 t + 3$ 
B)  $s = 4.9 t ^ { 2 } + 160 t + 3$ 
C)  $s = - 4.9 t ^ { 2 } + 160 t - 3$ 
D)  $s = - 4.9 t ^ { 2 } - 160 t + 3$ 
E)  $s = 4.9 t ^ { 2 } + 160 t - 3$ 
A)  $s = - 4.9 t ^ { 2 } + 160 t + 3$ 
B)  $s = 4.9 t ^ { 2 } + 160 t + 3$ 
C)  $s = - 4.9 t ^ { 2 } + 160 t - 3$ 
D)  $s = - 4.9 t ^ { 2 } - 160 t + 3$ 
E)  $s = 4.9 t ^ { 2 } + 160 t - 3$

Question 18

Let $V = \frac { 4 } { 3 } \pi r ^ { 3 }$ If $\frac { d r } { d t } = 2$ when $r = 1 \text {, }$ then $\frac { d V } { d t }$ is

Accepted Answer

A)  $16 \pi$ 
B)  $12 \pi$ 
C)  $8 \pi$ 
D)  $4 \pi$ 
E)  $2 \pi$ 
A)  $16 \pi$ 
B)  $12 \pi$ 
C)  $8 \pi$ 
D)  $4 \pi$ 
E)  $2 \pi$

Question 19

The antiderivative of $f ( x ) = - 4 ^ { x } + \sec ^ { 2 } x + \frac { 1 } { x \sqrt { x ^ { 2 } - 1 } }$ is

Accepted Answer

A)  $\frac { 4 ^ { x } } { \ln x } + \tan x + \sec ^ { - 1 } x + C$ 
B)  $- \frac { 4 ^ { x } } { \ln x } + \tan x - \sec ^ { - 1 } x + C$. 
C)  $- \frac { 4 ^ { x } } { \ln x } - \tan x + \sec ^ { - 1 } x + C$ 
D)  $- \frac { 4 ^ { x } } { \ln x } + \tan x + \sec ^ { - 1 } x + C$ 
E)  $- \frac { 4 ^ { x } } { \ln x } + \tan x - \sec ^ { - 1 } x + C$ 
A)  $\frac { 4 ^ { x } } { \ln x } + \tan x + \sec ^ { - 1 } x + C$ 
B)  $- \frac { 4 ^ { x } } { \ln x } + \tan x - \sec ^ { - 1 } x + C$. 
C)  $- \frac { 4 ^ { x } } { \ln x } - \tan x + \sec ^ { - 1 } x + C$ 
D)  $- \frac { 4 ^ { x } } { \ln x } + \tan x + \sec ^ { - 1 } x + C$ 
E)  $- \frac { 4 ^ { x } } { \ln x } + \tan x - \sec ^ { - 1 } x + C$

Question 20

The antiderivative of $f ( x ) = ( 2 x - 3 ) ( x + 4 )$ is

Accepted Answer

A)  $\frac { 2 } { 3 } x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } + 12 x + C$ 
B)  $\frac { 2 } { 3 } x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } - 12 x + C$. 
C)  $\frac { 2 } { 3 } x ^ { 3 } + \frac { 5 } { 2 } x ^ { 2 } - 12 x + C$ 
D)  $- \frac { 2 } { 3 } x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } + 12 x + C$ 
E)  $\frac { 2 } { 3 } x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } - 12 x + C$ 
A)  $\frac { 2 } { 3 } x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } + 12 x + C$ 
B)  $\frac { 2 } { 3 } x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } - 12 x + C$. 
C)  $\frac { 2 } { 3 } x ^ { 3 } + \frac { 5 } { 2 } x ^ { 2 } - 12 x + C$ 
D)  $- \frac { 2 } { 3 } x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } + 12 x + C$ 
E)  $\frac { 2 } { 3 } x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } - 12 x + C$

Let $f ( x ) = 2 x ^ { 3 } - 15 x ^ { 2 } - 36 x - 2$ Then ƒ has a relative minimum at x =

Let $f ( x ) = x + 2 + \frac { 3 } { x - 1 }$ on $[ 2,7 ]$ Then the set of all c in (2,7) guaranteed by the Mean Value Theorem is

The antiderivative of $f ( x ) = \frac { 1 } { 1 + x ^ { 2 } } + \frac { 2 } { x }$ is

A post office regulation is that the sum of the length and girth of a parcel must not exceed 6 feet. The largest volume in cubic feet of a parcel with square ends is

Let $f ( x ) = \sin x + \cos x$ on $[ 0,2 \pi ]$ Then the set of all in c guaranteed by Rolle's Theorem is

Let $f ( x ) = \ln x$ on $[ 1 , e ]$ Then the set of all c in (1,e) guaranteed by the Mean Value Theorem is

The particular solution of the differential equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } = 12 x ^ { 2 }$ satisfying the boundary conditions when x = 0, y = 1 and x = 3, y' = 8 is

The particular solution of the differential equation $\frac { d ^ { 2 } s } { d t ^ { 2 } } = 8 t - 3$ satisfying the initial conditions $\left. \frac { d s } { d t } \right| _ { x = 0 } = 4$ and $s ( 0 ) = 1$ is

The antiderivative of $f ( x ) = \frac { 3 x ^ { 2 } - 5 x + 7 } { 2 x }$ is

The smallest perimeter possible for a rectangle whose area is 400 square feet is

The largest set on which the function $f ( x ) = 3 \sin x$ on $[ 0,2 \pi ]$ is increasing is

The maximum area of a rectangular piece of land that can be enclosed by 100 yards of fencing is

Determine which of the following is not true for the graph of $f ( x ) = \frac { 2 x ^ { 2 } + x - 1 } { x ^ { 2 } - 1 }$

Let $f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } - 9 x + 1$ Then ƒ has a relative minimum at x =

The antiderivative of $f ( x ) = x ^ { 4 } + x - 3$ is

Let $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 15 x$ Then ƒ has a relative minimum at x =

The particular solution of the differential equation $\frac { d ^ { 2 } s } { d t ^ { 2 } } = - 9.8$ satisfying the initial conditions $\left[ \frac { d s } { d t } ( 0 ) \right] = 160$ and $s ( 0 ) = 3$ is

Let $V = \frac { 4 } { 3 } \pi r ^ { 3 }$ If $\frac { d r } { d t } = 2$ when $r = 1 \text {, }$ then $\frac { d V } { d t }$ is

The antiderivative of $f ( x ) = - 4 ^ { x } + \sec ^ { 2 } x + \frac { 1 } { x \sqrt { x ^ { 2 } - 1 } }$ is

The antiderivative of $f ( x ) = ( 2 x - 3 ) ( x + 4 )$ is

Preparing for Calculus

Limits and Continuity

The Derivative

More About Derivatives

The Integral

Applications of the Integral

Techniques of Integration

Infinite Series

Parametric Equations; Polar Equations

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

Exam 5: Applications of the Derivative

Let f(x)=2x3−15x2−36x−2f ( x ) = 2 x ^ { 3 } - 15 x ^ { 2 } - 36 x - 2f(x)=2x3−15x2−36x−2 Then ƒ has a relative minimum at x =

Let f(x)=x+2+3x−1f ( x ) = x + 2 + \frac { 3 } { x - 1 }f(x)=x+2+x−13​ on [2,7][ 2,7 ][2,7] Then the set of all c in (2,7) guaranteed by the Mean Value Theorem is

The antiderivative of f(x)=11+x2+2xf ( x ) = \frac { 1 } { 1 + x ^ { 2 } } + \frac { 2 } { x }f(x)=1+x21​+x2​ is

A post office regulation is that the sum of the length and girth of a parcel must not exceed 6 feet. The largest volume in cubic feet of a parcel with square ends is ​

Let f(x)=sin⁡x+cos⁡xf ( x ) = \sin x + \cos xf(x)=sinx+cosx on [0,2π][ 0,2 \pi ][0,2π] Then the set of all in c guaranteed by Rolle's Theorem is

Let f(x)=ln⁡xf ( x ) = \ln xf(x)=lnx on [1,e][ 1 , e ][1,e] Then the set of all c in (1,e) guaranteed by the Mean Value Theorem is

The particular solution of the differential equation d2ydx2=12x2\frac { d ^ { 2 } y } { d x ^ { 2 } } = 12 x ^ { 2 }dx2d2y​=12x2 satisfying the boundary conditions when x = 0, y = 1 and x = 3, y' = 8 is

The particular solution of the differential equation d2sdt2=8t−3\frac { d ^ { 2 } s } { d t ^ { 2 } } = 8 t - 3dt2d2s​=8t−3 satisfying the initial conditions dsdt∣x=0=4\left. \frac { d s } { d t } \right| _ { x = 0 } = 4dtds​​x=0​=4 and s(0)=1s ( 0 ) = 1s(0)=1 is

The antiderivative of f(x)=3x2−5x+72xf ( x ) = \frac { 3 x ^ { 2 } - 5 x + 7 } { 2 x }f(x)=2x3x2−5x+7​ is

The smallest perimeter possible for a rectangle whose area is 400 square feet is ​

The largest set on which the function f(x)=3sin⁡xf ( x ) = 3 \sin xf(x)=3sinx on [0,2π][ 0,2 \pi ][0,2π] is increasing is

The maximum area of a rectangular piece of land that can be enclosed by 100 yards of fencing is ​

Determine which of the following is not true for the graph of f(x)=2x2+x−1x2−1f ( x ) = \frac { 2 x ^ { 2 } + x - 1 } { x ^ { 2 } - 1 }f(x)=x2−12x2+x−1​

Let f(x)=−x3−6x2−9x+1f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } - 9 x + 1f(x)=−x3−6x2−9x+1 Then ƒ has a relative minimum at x =

The antiderivative of f(x)=x4+x−3f ( x ) = x ^ { 4 } + x - 3f(x)=x4+x−3 is

Let f(x)=x3−9x2+15xf ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 15 xf(x)=x3−9x2+15x Then ƒ has a relative minimum at x =

The particular solution of the differential equation d2sdt2=−9.8\frac { d ^ { 2 } s } { d t ^ { 2 } } = - 9.8dt2d2s​=−9.8 satisfying the initial conditions [dsdt(0)]=160\left[ \frac { d s } { d t } ( 0 ) \right] = 160[dtds​(0)]=160 and s(0)=3s ( 0 ) = 3s(0)=3 is

Let V=43πr3V = \frac { 4 } { 3 } \pi r ^ { 3 }V=34​πr3 If drdt=2\frac { d r } { d t } = 2dtdr​=2 when r=1, r = 1 \text {, }r=1, then dVdt\frac { d V } { d t }dtdV​ is

The antiderivative of f(x)=−4x+sec⁡2x+1xx2−1f ( x ) = - 4 ^ { x } + \sec ^ { 2 } x + \frac { 1 } { x \sqrt { x ^ { 2 } - 1 } }f(x)=−4x+sec2x+xx2−1​1​ is

The antiderivative of f(x)=(2x−3)(x+4)f ( x ) = ( 2 x - 3 ) ( x + 4 )f(x)=(2x−3)(x+4) is

Preparing for Calculus

Limits and Continuity

The Derivative

More About Derivatives

The Integral

Applications of the Integral

Techniques of Integration

Infinite Series

Parametric Equations; Polar Equations

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

Let $f ( x ) = 2 x ^ { 3 } - 15 x ^ { 2 } - 36 x - 2$ Then ƒ has a relative minimum at x =

Let $f ( x ) = x + 2 + \frac { 3 } { x - 1 }$ on $[ 2,7 ]$ Then the set of all c in (2,7) guaranteed by the Mean Value Theorem is

The antiderivative of $f ( x ) = \frac { 1 } { 1 + x ^ { 2 } } + \frac { 2 } { x }$ is

A post office regulation is that the sum of the length and girth of a parcel must not exceed 6 feet. The largest volume in cubic feet of a parcel with square ends is

Let $f ( x ) = \sin x + \cos x$ on $[ 0,2 \pi ]$ Then the set of all in c guaranteed by Rolle's Theorem is

Let $f ( x ) = \ln x$ on $[ 1 , e ]$ Then the set of all c in (1,e) guaranteed by the Mean Value Theorem is

The particular solution of the differential equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } = 12 x ^ { 2 }$ satisfying the boundary conditions when x = 0, y = 1 and x = 3, y' = 8 is

The particular solution of the differential equation $\frac { d ^ { 2 } s } { d t ^ { 2 } } = 8 t - 3$ satisfying the initial conditions $\left. \frac { d s } { d t } \right| _ { x = 0 } = 4$ and $s ( 0 ) = 1$ is

The antiderivative of $f ( x ) = \frac { 3 x ^ { 2 } - 5 x + 7 } { 2 x }$ is

The smallest perimeter possible for a rectangle whose area is 400 square feet is

The largest set on which the function $f ( x ) = 3 \sin x$ on $[ 0,2 \pi ]$ is increasing is

The maximum area of a rectangular piece of land that can be enclosed by 100 yards of fencing is

Determine which of the following is not true for the graph of $f ( x ) = \frac { 2 x ^ { 2 } + x - 1 } { x ^ { 2 } - 1 }$

Let $f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } - 9 x + 1$ Then ƒ has a relative minimum at x =

The antiderivative of $f ( x ) = x ^ { 4 } + x - 3$ is

Let $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 15 x$ Then ƒ has a relative minimum at x =

The particular solution of the differential equation $\frac { d ^ { 2 } s } { d t ^ { 2 } } = - 9.8$ satisfying the initial conditions $\left[ \frac { d s } { d t } ( 0 ) \right] = 160$ and $s ( 0 ) = 3$ is

Let $V = \frac { 4 } { 3 } \pi r ^ { 3 }$ If $\frac { d r } { d t } = 2$ when $r = 1 \text {, }$ then $\frac { d V } { d t }$ is

The antiderivative of $f ( x ) = - 4 ^ { x } + \sec ^ { 2 } x + \frac { 1 } { x \sqrt { x ^ { 2 } - 1 } }$ is

The antiderivative of $f ( x ) = ( 2 x - 3 ) ( x + 4 )$ is