A ball is dropped from a window 80 feet above the ground.Assume that its acceleration is a(t)= -32 ft/sec2 for t $\ge$ 0.After how many seconds does it hit the ground? Round to 2 decimal places.

The answer of A ball is dropped from a window...

You decide to take a trip down a stretch of road that runs straight east and west.The following table gives your eastward velocity (in miles per minute)measured at one-minute intervals for the first ten minutes of your trip. $\begin{array}{cccccccccccc} \text { Time (min) } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \text { Velocity } & 0.00 & 0.60 & 1.02 & 1.27 & 1.36 & 1.27 & 1.02 & 0.60 & 0.00 & -0.77 & -1.70 \\ \text { (mi/min)} \end{array}$ What is your best estimate of the total eastward distance of your car from your starting position after ten minutes? Round to the nearest whole number.

The answer of You decide to take a trip down...

Exam 6: Constructing Antiderivatives

On the moon the acceleration due to gravity is 5 feet/ sec².A brick is dropped from the top of a tower on the moon and hits the ground in 16 seconds.How many feet high is the tower?

(Short Answer)

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Question 41

Find a function F such that $F^{\prime}(x)=\sin x+\frac{7}{x}$ .

(Multiple Choice)

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Question 42

A ball is dropped from a window 80 feet above the ground.Assume that its acceleration is a(t)= -32 ft/sec²for t $\ge$ 0.After how many seconds does it hit the ground? Round to 2 decimal places.

(Short Answer)

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Question 43

Evaluate $\frac{d}{d x} \int_{3^{n}}^{0} t d t$ .

(Essay)

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Question 44

On planet Janet the gravitational constant g is -11 feet per second per second: that is, for every second an object falls it picks up an extra 11 feet per second of velocity downward.A ball is thrown upward at time t = 0 at 44 feet per second.After how many seconds does the ball reach the peak of its flight?

(Short Answer)

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Question 45

Is the antiderivative for $h(x)=\frac{a}{x}+\sin \alpha x$ , where a is a constant, given by $\ln |x|-\frac{1}{a} \cos \alpha x+C$ ?

(True/False)

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Question 46

A dog's bone is tossed in a yard traveling with a vertical velocity of $v(t)=-32 t+2$ feet/sec.Determine the maximum height reached by the bone.

(Short Answer)

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Question 47

Sketch the graphs of $y=e^{x}$ and y = ex.For which values of x is $e^{x}>e x$ ? Mark all that apply.

(Multiple Choice)

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Question 48

Find an antiderivative of $\frac{5}{x}+\frac{x}{5}$ .

(Multiple Choice)

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Question 49

Find an antiderivative F(x)with F'(x)= f (x)and F(0)= 3 when $f(x)=\sin x-\cos x$ .

(Essay)

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Question 50

You decide to take a trip down a stretch of road that runs straight east and west.The following table gives your eastward velocity (in miles per minute)measured at one-minute intervals for the first ten minutes of your trip. Time (min) 0 1 2 3 4 5 6 7 8 9 10 Velocity 0.00 0.60 1.02 1.27 1.36 1.27 1.02 0.60 0.00 -0.77 -1.70 (mi/min) What is your best estimate of the total eastward distance of your car from your starting position after ten minutes? Round to the nearest whole number.

(Short Answer)

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Question 51

A boat has constant deceleration.It was initially moving at 80 mph and stopped in a distance of 300 feet.The rate of deceleration is _____ ft/ sec².(Note: 1 mph = 22/15 ft/ sec.)Round to 2 decimal places.

(Short Answer)

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Question 52

Below are the graphs of (i) $f(x)$ , (ii) $f^{\prime}(x)$ , and (iii) $\int_{0}^{x} f(t) d t$ (not necessarily in that order). $Below are the graphs of (i) f(x) , (ii) f^{\prime}(x) , and (iii) \int_{0}^{x} f(t) d t (not necessarily in that order). Which one is the graph of (iii)?$ $Below are the graphs of (i) f(x) , (ii) f^{\prime}(x) , and (iii) \int_{0}^{x} f(t) d t (not necessarily in that order). Which one is the graph of (iii)?$ $Below are the graphs of (i) f(x) , (ii) f^{\prime}(x) , and (iii) \int_{0}^{x} f(t) d t (not necessarily in that order). Which one is the graph of (iii)?$ Which one is the graph of (iii)?

(Multiple Choice)

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Question 53

An object falls from the top of an 600 foot building.How fast is it going when it hits the ground? Round to 2 decimal places.

(Short Answer)

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Question 54

Estimate $\int_{-4}^{2} f(x) d x$ for the figure given. $Estimate \int_{-4}^{2} f(x) d x for the figure given.$

(Short Answer)

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Question 55

Sketch a graph of the antiderivative of g(x), given the graph g'(x)and g(0)=1.

(Essay)

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Question 56

A particle is traveling along a straight line.(Positive velocities indicate movement to the right.)Indicate on the graph where the particle has had a change in position of 3 units.

(Short Answer)

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Question 57

If $f(x)$ is as shown in the first graph, could the function in the second graph represent the total area (i.e., not necessarily the definite integral)between f(x)and the x-axis from 0 to a?

(True/False)

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Question 58

On planet Janet the gravitational constant g is -10 feet per second per second: that is, for every second an object falls it picks up an extra 10 feet per second of velocity downward.A ball is thrown upward (from height zero)at time t = 0 at 40 feet per second.What is the peak height of the ball?

(Short Answer)

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Question 59

Is the antiderivative for $k(x)=\frac{6}{x}+6 e^{6 x}$ given by $6 \ln |x|+e^{6 x}+C$ ?

(True/False)

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Question 60

Showing 41 - 60 of 90

On the moon the acceleration due to gravity is 5 feet/ sec².A brick is dropped from the top of a tower on the moon and hits the ground in 16 seconds.How many feet high is the tower?

Find a function F such that $F^{\prime}(x)=\sin x+\frac{7}{x}$ .

A ball is dropped from a window 80 feet above the ground.Assume that its acceleration is a(t)= -32 ft/sec²for t $\ge$ 0.After how many seconds does it hit the ground? Round to 2 decimal places.

Evaluate $\frac{d}{d x} \int_{3^{n}}^{0} t d t$ .

Is the antiderivative for $h(x)=\frac{a}{x}+\sin \alpha x$ , where a is a constant, given by $\ln |x|-\frac{1}{a} \cos \alpha x+C$ ?

A dog's bone is tossed in a yard traveling with a vertical velocity of $v(t)=-32 t+2$ feet/sec.Determine the maximum height reached by the bone.

Sketch the graphs of $y=e^{x}$ and y = ex.For which values of x is $e^{x}>e x$ ? Mark all that apply.

Find an antiderivative of $\frac{5}{x}+\frac{x}{5}$ .

Find an antiderivative F(x)with F'(x)= f (x)and F(0)= 3 when $f(x)=\sin x-\cos x$ .

A boat has constant deceleration.It was initially moving at 80 mph and stopped in a distance of 300 feet.The rate of deceleration is _____ ft/ sec².(Note: 1 mph = 22/15 ft/ sec.)Round to 2 decimal places.

An object falls from the top of an 600 foot building.How fast is it going when it hits the ground? Round to 2 decimal places.

Estimate $\int_{-4}^{2} f(x) d x$ for the figure given. $Estimate \int_{-4}^{2} f(x) d x for the figure given.$

Sketch a graph of the antiderivative of g(x), given the graph g'(x)and g(0)=1.

A particle is traveling along a straight line.(Positive velocities indicate movement to the right.)Indicate on the graph where the particle has had a change in position of 3 units.

If $f(x)$ is as shown in the first graph, could the function in the second graph represent the total area (i.e., not necessarily the definite integral)between f(x)and the x-axis from 0 to a?

On planet Janet the gravitational constant g is -10 feet per second per second: that is, for every second an object falls it picks up an extra 10 feet per second of velocity downward.A ball is thrown upward (from height zero)at time t = 0 at 40 feet per second.What is the peak height of the ball?

Is the antiderivative for $k(x)=\frac{6}{x}+6 e^{6 x}$ given by $6 \ln |x|+e^{6 x}+C$ ?

A Library of Functions

Key Concept: the Derivative

Short-Cuts to Differentiation

Using the Derivative

Key Concept- the Definite Integral

Integration

Using the Definite Integral

Sequences and Series

Approximating Functions Using Series

Differential Equations

Functions of Several Variables

A Fundamental Tool- Vectors

Differentiating Functions of Several Variables

Optimization- Local and Global Extrema

Integrating Functions of Several Variables

Parameterization and Vector Fields

Line Integrals

Flux Integrals and Divergence

The Curl and Stokes Theorem

Parameters, Coordinates, Integrals

Filters

Exam 6: Constructing Antiderivatives

On the moon the acceleration due to gravity is 5 feet/ sec2.A brick is dropped from the top of a tower on the moon and hits the ground in 16 seconds.How many feet high is the tower?

Find a function F such that F′(x)=sin⁡x+7xF^{\prime}(x)=\sin x+\frac{7}{x}F′(x)=sinx+x7​ .

A ball is dropped from a window 80 feet above the ground.Assume that its acceleration is a(t)= -32 ft/sec2 for t ≥\ge≥ 0.After how many seconds does it hit the ground? Round to 2 decimal places.

Evaluate ddx∫3n0tdt\frac{d}{d x} \int_{3^{n}}^{0} t d tdxd​∫3n0​tdt .

Is the antiderivative for h(x)=ax+sin⁡αxh(x)=\frac{a}{x}+\sin \alpha xh(x)=xa​+sinαx , where a is a constant, given by ln⁡∣x∣−1acos⁡αx+C\ln |x|-\frac{1}{a} \cos \alpha x+Cln∣x∣−a1​cosαx+C ?

A dog's bone is tossed in a yard traveling with a vertical velocity of v(t)=−32t+2v(t)=-32 t+2v(t)=−32t+2 feet/sec.Determine the maximum height reached by the bone.

Sketch the graphs of y=exy=e^{x}y=ex and y = ex.For which values of x is ex>exe^{x}>e xex>ex ? Mark all that apply.

Find an antiderivative of 5x+x5\frac{5}{x}+\frac{x}{5}x5​+5x​ .

Find an antiderivative F(x)with F'(x)= f (x)and F(0)= 3 when f(x)=sin⁡x−cos⁡xf(x)=\sin x-\cos xf(x)=sinx−cosx .

A boat has constant deceleration.It was initially moving at 80 mph and stopped in a distance of 300 feet.The rate of deceleration is _____ ft/ sec2.(Note: 1 mph = 22/15 ft/ sec.)Round to 2 decimal places.

Below are the graphs of (i) f(x)f(x)f(x) , (ii) f′(x)f^{\prime}(x)f′(x) , and (iii) ∫0xf(t)dt\int_{0}^{x} f(t) d t∫0x​f(t)dt (not necessarily in that order). Which one is the graph of (iii)?

An object falls from the top of an 600 foot building.How fast is it going when it hits the ground? Round to 2 decimal places.

Estimate ∫−42f(x)dx\int_{-4}^{2} f(x) d x∫−42​f(x)dx for the figure given.

Sketch a graph of the antiderivative of g(x), given the graph g'(x)and g(0)=1.

A particle is traveling along a straight line.(Positive velocities indicate movement to the right.)Indicate on the graph where the particle has had a change in position of 3 units.

If f(x)f(x)f(x) is as shown in the first graph, could the function in the second graph represent the total area (i.e., not necessarily the definite integral)between f(x)and the x-axis from 0 to a?

On planet Janet the gravitational constant g is -10 feet per second per second: that is, for every second an object falls it picks up an extra 10 feet per second of velocity downward.A ball is thrown upward (from height zero)at time t = 0 at 40 feet per second.What is the peak height of the ball?

Is the antiderivative for k(x)=6x+6e6xk(x)=\frac{6}{x}+6 e^{6 x}k(x)=x6​+6e6x given by 6ln⁡∣x∣+e6x+C6 \ln |x|+e^{6 x}+C6ln∣x∣+e6x+C ?

A Library of Functions

Key Concept: the Derivative

Short-Cuts to Differentiation

Using the Derivative

Key Concept- the Definite Integral

Integration

Using the Definite Integral

Sequences and Series

Approximating Functions Using Series

Differential Equations

Functions of Several Variables

A Fundamental Tool- Vectors

Differentiating Functions of Several Variables

Optimization- Local and Global Extrema

Integrating Functions of Several Variables

Parameterization and Vector Fields

Line Integrals

Flux Integrals and Divergence

The Curl and Stokes Theorem

Parameters, Coordinates, Integrals

Filters

On the moon the acceleration due to gravity is 5 feet/ sec².A brick is dropped from the top of a tower on the moon and hits the ground in 16 seconds.How many feet high is the tower?

Find a function F such that $F^{\prime}(x)=\sin x+\frac{7}{x}$ .

A ball is dropped from a window 80 feet above the ground.Assume that its acceleration is a(t)= -32 ft/sec²for t $\ge$ 0.After how many seconds does it hit the ground? Round to 2 decimal places.

Evaluate $\frac{d}{d x} \int_{3^{n}}^{0} t d t$ .

Is the antiderivative for $h(x)=\frac{a}{x}+\sin \alpha x$ , where a is a constant, given by $\ln |x|-\frac{1}{a} \cos \alpha x+C$ ?

A dog's bone is tossed in a yard traveling with a vertical velocity of $v(t)=-32 t+2$ feet/sec.Determine the maximum height reached by the bone.

Sketch the graphs of $y=e^{x}$ and y = ex.For which values of x is $e^{x}>e x$ ? Mark all that apply.

Find an antiderivative of $\frac{5}{x}+\frac{x}{5}$ .

Find an antiderivative F(x)with F'(x)= f (x)and F(0)= 3 when $f(x)=\sin x-\cos x$ .

A boat has constant deceleration.It was initially moving at 80 mph and stopped in a distance of 300 feet.The rate of deceleration is _____ ft/ sec².(Note: 1 mph = 22/15 ft/ sec.)Round to 2 decimal places.

Estimate $\int_{-4}^{2} f(x) d x$ for the figure given. $Estimate \int_{-4}^{2} f(x) d x for the figure given.$

If $f(x)$ is as shown in the first graph, could the function in the second graph represent the total area (i.e., not necessarily the definite integral)between f(x)and the x-axis from 0 to a?

Is the antiderivative for $k(x)=\frac{6}{x}+6 e^{6 x}$ given by $6 \ln |x|+e^{6 x}+C$ ?