Exam 14: Vector-Valued Functions

Solve the problem. Assume the x-axis is horizontal, the positive y-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the objects -A projectile is fired at a speed of 800 m/sec at an angle of 34°. How long will it take to get 20 km downrange? Round your answer to the nearest whole number.

(Multiple Choice)

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Question 41

Find a function r(t) that describes the line or line segment. -The line segment from P(2, 7, 3) to Q(3, 1, 1)

(Multiple Choice)

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Question 42

Find a function r(t) that describes the curve where the surfaces intersect. - + = 16; z = 2x + 3y

(Multiple Choice)

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Question 43

Evaluate the limit. - = ( 7 cos ti+ 6 sin tj)

(Multiple Choice)

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Question 44

The position vector of a particle is r(t). Find the requested vector. -

(Multiple Choice)

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Question 45

Evaluate the integral. -

(Multiple Choice)

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Question 46

Find the unit tangent vector of the given curve. -r(t) = ( 6 - 2t)i + (2t - 9)j + ( 9 + t)k

(Multiple Choice)

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Question 47

Solve the problem. Assume the x-axis is horizontal, the positive y-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the objects -A projectile is fired with an initial speed of 585 m/sec at an angle of 45°. What is the greatest height reached by the projectile? Round your answer to the nearest tenth.

(Multiple Choice)

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Question 48

Find the domain of the vector-valued function. -r(t) = i + j

(Multiple Choice)

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Question 49

The position vector of a particle is r(t). Find the requested vector. -

(Multiple Choice)

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Question 50

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. -Find the acceleration vector. r(t) = ( 7 ln( 5t))i + ( 3 )j

(Multiple Choice)

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Question 51

FInd the tangential and normal components of the acceleration. -r(t) = ( 8t sin t + 8 cos t)i + ( 8t cos t - 8 sin t)j + 8k

(Multiple Choice)

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Question 52

Verify that the curve r(t) lies on the surface. Give the name of the surface. -r(t) = (2t cos t)i + (2t sin t)j + 2t k; + =

(Multiple Choice)

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Question 53

Find the curvature of the space curve. -r(t) = ti + (sinh t)j + (cosh t)k

(Multiple Choice)

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Question 54

Find the unit tangent vector T and the principal unit normal vector N. -r(t) = i + j + 3tk

(Multiple Choice)

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Question 55

Find the unit tangent vector T and the principal unit normal vector N. -r(t) = ( 3 + t)i + ( 7 + ln(sec t))j - 3k, - $\pi$ /2 < t < $\pi$ /2

(Multiple Choice)

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Question 56

Find the unit tangent vector of the given curve. -r(t) = ( 8t cos t - 8 sin t)j + ( 8t sin t + 8 cos t)k

(Multiple Choice)

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Question 57

Evaluate the integral. -

(Multiple Choice)

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Question 58

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. -Find the velocity vector.

(Multiple Choice)

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Question 59

Graph the curve described by the function, indicating the positive orientation. -r(t) = 2cos t i + 3j + 2 sin t k, for 0 $\le$ t $\le$ 2 $\pi$

(Multiple Choice)

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Question 60

Showing 41 - 60 of 83

Find a function r(t) that describes the line or line segment. -The line segment from P(2, 7, 3) to Q(3, 1, 1)

Find a function r(t) that describes the curve where the surfaces intersect. - + = 16; z = 2x + 3y

Evaluate the limit. - = ( 7 cos ti+ 6 sin tj)

The position vector of a particle is r(t). Find the requested vector. -

Evaluate the integral. -

Find the unit tangent vector of the given curve. -r(t) = ( 6 - 2t)i + (2t - 9)j + ( 9 + t)k

Find the domain of the vector-valued function. -r(t) = i + j

The position vector of a particle is r(t). Find the requested vector. -

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. -Find the acceleration vector. r(t) = ( 7 ln( 5t))i + ( 3 )j

FInd the tangential and normal components of the acceleration. -r(t) = ( 8t sin t + 8 cos t)i + ( 8t cos t - 8 sin t)j + 8k

Verify that the curve r(t) lies on the surface. Give the name of the surface. -r(t) = (2t cos t)i + (2t sin t)j + 2t k; + =

Find the curvature of the space curve. -r(t) = ti + (sinh t)j + (cosh t)k

Find the unit tangent vector T and the principal unit normal vector N. -r(t) = i + j + 3tk

Find the unit tangent vector T and the principal unit normal vector N. -r(t) = ( 3 + t)i + ( 7 + ln(sec t))j - 3k, - $\pi$ /2 < t < $\pi$ /2

Find the unit tangent vector of the given curve. -r(t) = ( 8t cos t - 8 sin t)j + ( 8t sin t + 8 cos t)k

Evaluate the integral. -

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. -Find the velocity vector.

Graph the curve described by the function, indicating the positive orientation. -r(t) = 2cos t i + 3j + 2 sin t k, for 0 $\le$ t $\le$ 2 $\pi$

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Exam 14: Vector-Valued Functions

Find a function r(t) that describes the line or line segment. -The line segment from P(2, 7, 3) to Q(3, 1, 1)

Find a function r(t) that describes the curve where the surfaces intersect. - + = 16; z = 2x + 3y

Evaluate the limit. - = ( 7 cos ti+ 6 sin tj)

The position vector of a particle is r(t). Find the requested vector. -

Evaluate the integral. -

Find the unit tangent vector of the given curve. -r(t) = ( 6 - 2t)i + (2t - 9)j + ( 9 + t)k

Find the domain of the vector-valued function. -r(t) = i + j

The position vector of a particle is r(t). Find the requested vector. -

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. -Find the acceleration vector. r(t) = ( 7 ln( 5t))i + ( 3 )j

FInd the tangential and normal components of the acceleration. -r(t) = ( 8t sin t + 8 cos t)i + ( 8t cos t - 8 sin t)j + 8k

Verify that the curve r(t) lies on the surface. Give the name of the surface. -r(t) = (2t cos t)i + (2t sin t)j + 2t k; + =

Find the curvature of the space curve. -r(t) = ti + (sinh t)j + (cosh t)k

Find the unit tangent vector T and the principal unit normal vector N. -r(t) = i + j + 3tk

Find the unit tangent vector T and the principal unit normal vector N. -r(t) = ( 3 + t)i + ( 7 + ln(sec t))j - 3k, - π\piπ /2 < t < π\piπ /2

Find the unit tangent vector of the given curve. -r(t) = ( 8t cos t - 8 sin t)j + ( 8t sin t + 8 cos t)k

Evaluate the integral. -

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. -Find the velocity vector.

Graph the curve described by the function, indicating the positive orientation. -r(t) = 2cos t i + 3j + 2 sin t k, for 0 ≤\le≤ t ≤\le≤ 2 π\piπ

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Find the unit tangent vector T and the principal unit normal vector N. -r(t) = ( 3 + t)i + ( 7 + ln(sec t))j - 3k, - $\pi$ /2 < t < $\pi$ /2

Graph the curve described by the function, indicating the positive orientation. -r(t) = 2cos t i + 3j + 2 sin t k, for 0 $\le$ t $\le$ 2 $\pi$