Exam 5: Applications of the Derivative

A rectangular plot of farmland is enclosed on one side by a river and on the other three sides by an electric fence. With 800 meters of wire for fencing, the maximum area can be enclosed is

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Question 141

Determine the value of the limit $\lim _ { x \rightarrow 0 } \frac { 1 - \cos x } { x \sin x }$ ?

(Multiple Choice)

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Question 142

Determine which of the following is not true for the graph of $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 x$

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Question 143

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

(Multiple Choice)

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Question 144

Let $f ( x ) = x ^ { 3 } - 4 x$ on $[ - 2,2 ]$ Then the set of all c in (-2,2) guaranteed by Rolle's Theorem is

(Multiple Choice)

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Question 145

Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$ Then ƒ has a relative minimum at x =

(Multiple Choice)

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Question 146

Determine the value of the limit $\lim _ { x \rightarrow 1 } \frac { x - 1 } { \ln x - \sin ( 2 \pi x ) }$

(Multiple Choice)

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Question 147

Determine the value of the limit $\lim _ { x \rightarrow 0 ^ { + } } \left( \frac { \ln x } { \frac { 1 } { x } } \right)$

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Question 148

Let $x \cos y = 5$ If $\frac { d x } { d t } = - 4$ when $y = - \frac { \pi } { 3 } ,$ then $\frac { d y } { d t }$ is

(Multiple Choice)

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Question 149

Determine which of the following is not true for the graph of $f ( x ) = 2 x - 3 x ^ { \frac { 2 } { 3 } } + 4$

(Multiple Choice)

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Question 150

Let $f ( x ) = 2 x ^ { 3 } - 24 x$ Then ƒ has a point of inflection at x =

(Multiple Choice)

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Question 151

The particular solution of the differential equation $\left( d ^ { 2 } y \right) / \left( d x ^ { 2 } \right) = 2 - 6 x$ satisfying the boundary conditions when $y ^ { \prime } ( 0 ) = 4$ and $y ( 0 ) = 1$ is

(Multiple Choice)

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Question 152

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

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Question 153

Determine which of the following is not true for the graph of $f ( x ) = x ^ { 4 } + 2 x ^ { 3 }$

(Multiple Choice)

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Question 154

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

(Multiple Choice)

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Question 155

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

(Multiple Choice)

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Question 156

The largest set on which the function $f ( x ) = 5 ^ { - x }$ is decreasing is

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Question 157

Let $f ( x ) = \frac { 1 } { 4 } x ^ { 4 } - \frac { 1 } { 3 } x ^ { 3 } - x ^ { 2 } + 1$ on $[ - 2,3 ]$ The absolute minimum and maximum of ƒ are located respectively at x =

(Multiple Choice)

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Question 158

The particular solution of the differential equation $\frac { d y } { d x } = 5 x ^ { 2 } + 2$ satisfying the boundary condition when x = 3, y = 5 is

(Multiple Choice)

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Question 159

Let $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 3$ Then ƒ has a relative minimum at x =

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Question 160

A rectangular plot of farmland is enclosed on one side by a river and on the other three sides by an electric fence. With 800 meters of wire for fencing, the maximum area can be enclosed is

Determine the value of the limit $\lim _ { x \rightarrow 0 } \frac { 1 - \cos x } { x \sin x }$ ?

Determine which of the following is not true for the graph of $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 x$

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

Let $f ( x ) = x ^ { 3 } - 4 x$ on $[ - 2,2 ]$ Then the set of all c in (-2,2) guaranteed by Rolle's Theorem is

Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$ Then ƒ has a relative minimum at x =

Determine the value of the limit $\lim _ { x \rightarrow 1 } \frac { x - 1 } { \ln x - \sin ( 2 \pi x ) }$

Determine the value of the limit $\lim _ { x \rightarrow 0 ^ { + } } \left( \frac { \ln x } { \frac { 1 } { x } } \right)$

Let $x \cos y = 5$ If $\frac { d x } { d t } = - 4$ when $y = - \frac { \pi } { 3 } ,$ then $\frac { d y } { d t }$ is

Determine which of the following is not true for the graph of $f ( x ) = 2 x - 3 x ^ { \frac { 2 } { 3 } } + 4$

Let $f ( x ) = 2 x ^ { 3 } - 24 x$ Then ƒ has a point of inflection at x =

The particular solution of the differential equation $\left( d ^ { 2 } y \right) / \left( d x ^ { 2 } \right) = 2 - 6 x$ satisfying the boundary conditions when $y ^ { \prime } ( 0 ) = 4$ and $y ( 0 ) = 1$ is

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

Determine which of the following is not true for the graph of $f ( x ) = x ^ { 4 } + 2 x ^ { 3 }$

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

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

The largest set on which the function $f ( x ) = 5 ^ { - x }$ is decreasing is

Let $f ( x ) = \frac { 1 } { 4 } x ^ { 4 } - \frac { 1 } { 3 } x ^ { 3 } - x ^ { 2 } + 1$ on $[ - 2,3 ]$ The absolute minimum and maximum of ƒ are located respectively at x =

The particular solution of the differential equation $\frac { d y } { d x } = 5 x ^ { 2 } + 2$ satisfying the boundary condition when x = 3, y = 5 is

Let $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 3$ Then ƒ has a relative minimum at x =

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

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Exam 5: Applications of the Derivative

A rectangular plot of farmland is enclosed on one side by a river and on the other three sides by an electric fence. With 800 meters of wire for fencing, the maximum area can be enclosed is ​

Determine the value of the limit lim⁡x→01−cos⁡xxsin⁡x\lim _ { x \rightarrow 0 } \frac { 1 - \cos x } { x \sin x }limx→0​xsinx1−cosx​ ?

Determine which of the following is not true for the graph of f(x)=x3−6x2+9xf ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 xf(x)=x3−6x2+9x

The antiderivative of f(x)=5x−3x2f ( x ) = 5 \sqrt { x } - 3 x ^ { 2 }f(x)=5x​−3x2 is

Let f(x)=x3−4xf ( x ) = x ^ { 3 } - 4 xf(x)=x3−4x on [−2,2][ - 2,2 ][−2,2] Then the set of all c in (-2,2) guaranteed by Rolle's Theorem is

Let f(x)=x3−x2−x+8f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8f(x)=x3−x2−x+8 Then ƒ has a relative minimum at x =

Determine the value of the limit lim⁡x→1x−1ln⁡x−sin⁡(2πx)\lim _ { x \rightarrow 1 } \frac { x - 1 } { \ln x - \sin ( 2 \pi x ) }limx→1​lnx−sin(2πx)x−1​

Determine the value of the limit lim⁡x→0+(ln⁡x1x)\lim _ { x \rightarrow 0 ^ { + } } \left( \frac { \ln x } { \frac { 1 } { x } } \right)limx→0+​(x1​lnx​)

Let xcos⁡y=5x \cos y = 5xcosy=5 If dxdt=−4\frac { d x } { d t } = - 4dtdx​=−4 when y=−π3,y = - \frac { \pi } { 3 } ,y=−3π​, then dydt\frac { d y } { d t }dtdy​ is

Determine which of the following is not true for the graph of f(x)=2x−3x23+4f ( x ) = 2 x - 3 x ^ { \frac { 2 } { 3 } } + 4f(x)=2x−3x32​+4

Let f(x)=2x3−24xf ( x ) = 2 x ^ { 3 } - 24 xf(x)=2x3−24x Then ƒ has a point of inflection at x =

The particular solution of the differential equation (d2y)/(dx2)=2−6x\left( d ^ { 2 } y \right) / \left( d x ^ { 2 } \right) = 2 - 6 x(d2y)/(dx2)=2−6x satisfying the boundary conditions when y′(0)=4y ^ { \prime } ( 0 ) = 4y′(0)=4 and y(0)=1y ( 0 ) = 1y(0)=1 is

The antiderivative of f(x)=2x−x2−1x2f ( x ) = 2 ^ { x } - x ^ { 2 } - \frac { 1 } { x ^ { 2 } }f(x)=2x−x2−x21​ is

Determine which of the following is not true for the graph of f(x)=x4+2x3f ( x ) = x ^ { 4 } + 2 x ^ { 3 }f(x)=x4+2x3

The antiderivative of f(x)=cos⁡x−41−x2f ( x ) = \cos x - \frac { 4 } { \sqrt { 1 - x ^ { 2 } } }f(x)=cosx−1−x2​4​ is

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 point of inflection at x =

The largest set on which the function f(x)=5−xf ( x ) = 5 ^ { - x }f(x)=5−x is decreasing is

Let f(x)=14x4−13x3−x2+1f ( x ) = \frac { 1 } { 4 } x ^ { 4 } - \frac { 1 } { 3 } x ^ { 3 } - x ^ { 2 } + 1f(x)=41​x4−31​x3−x2+1 on [−2,3][ - 2,3 ][−2,3] The absolute minimum and maximum of ƒ are located respectively at x =

The particular solution of the differential equation dydx=5x2+2\frac { d y } { d x } = 5 x ^ { 2 } + 2dxdy​=5x2+2 satisfying the boundary condition when x = 3, y = 5 is

Let f(x)=x4−2x3+3f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 3f(x)=x4−2x3+3 Then ƒ has a relative minimum at x =

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

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A rectangular plot of farmland is enclosed on one side by a river and on the other three sides by an electric fence. With 800 meters of wire for fencing, the maximum area can be enclosed is

Determine the value of the limit $\lim _ { x \rightarrow 0 } \frac { 1 - \cos x } { x \sin x }$ ?

Determine which of the following is not true for the graph of $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 x$

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

Let $f ( x ) = x ^ { 3 } - 4 x$ on $[ - 2,2 ]$ Then the set of all c in (-2,2) guaranteed by Rolle's Theorem is

Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$ Then ƒ has a relative minimum at x =

Determine the value of the limit $\lim _ { x \rightarrow 1 } \frac { x - 1 } { \ln x - \sin ( 2 \pi x ) }$

Determine the value of the limit $\lim _ { x \rightarrow 0 ^ { + } } \left( \frac { \ln x } { \frac { 1 } { x } } \right)$

Let $x \cos y = 5$ If $\frac { d x } { d t } = - 4$ when $y = - \frac { \pi } { 3 } ,$ then $\frac { d y } { d t }$ is

Determine which of the following is not true for the graph of $f ( x ) = 2 x - 3 x ^ { \frac { 2 } { 3 } } + 4$

Let $f ( x ) = 2 x ^ { 3 } - 24 x$ Then ƒ has a point of inflection at x =

The particular solution of the differential equation $\left( d ^ { 2 } y \right) / \left( d x ^ { 2 } \right) = 2 - 6 x$ satisfying the boundary conditions when $y ^ { \prime } ( 0 ) = 4$ and $y ( 0 ) = 1$ is

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

Determine which of the following is not true for the graph of $f ( x ) = x ^ { 4 } + 2 x ^ { 3 }$

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

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

The largest set on which the function $f ( x ) = 5 ^ { - x }$ is decreasing is

Let $f ( x ) = \frac { 1 } { 4 } x ^ { 4 } - \frac { 1 } { 3 } x ^ { 3 } - x ^ { 2 } + 1$ on $[ - 2,3 ]$ The absolute minimum and maximum of ƒ are located respectively at x =

The particular solution of the differential equation $\frac { d y } { d x } = 5 x ^ { 2 } + 2$ satisfying the boundary condition when x = 3, y = 5 is

Let $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 3$ Then ƒ has a relative minimum at x =