Question 1

Find the derivative of the function.

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Question 2

Evaluate the integral.

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Question 3

The depth of water   at my favorite surfing spot varies from 5 to 15 feet, depending on the time. Last Sunday high tide occurred at 5:00 A.M. and the next high tide occurred at 6:30 P.M. Use a sine function to model to the depth of water as a function of time t in hours since midnight in Sunday morning.

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The answer of The depth of water   at...

Question 4

Find the derivative of the function.

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Question 5

Find the derivative of the function.

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Question 6

Recall that the average of a function   on an interval   is   Calculate the 2-unit moving average of the function.

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Question 7

Evaluate the integral.

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Question 8

Model the curve with a sine function.   Note that the period of the curve is   and its range is 2.2, 2.2 and the graph of the sine function is shifted to the left 0.9 units.

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Question 9

Model the curve with a sine function.   Note that the period of the curve is   and its range is   , the graph of the sine function is shifted to the right 3 units.

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Question 10

Model the curve with a cosine function.   Note that the period of the curve is   , its range is   and the graph of the cosine function is shifted upward 65 units and shifted to the right 9 units. Write the model function as a function of (x)and   .

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The answer of Model the curve with a cosine function....

Question 11

Sales of computers are subject to seasonal fluctuations. Computer City s sales of computers in 1995 and 1996 can be approximated by the function   where   is time in quarters   represents the end of the first quarter of 1995)and   is computer sales (quarterly revenue)in billions of dollars. Estimate Computer City s maximum and minimum quarterly revenue from computer sales. Maximum sales __________ billions of dollars Minimum sales __________ billions of dollars

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The answer of Sales of computers are subject to seasonal...

Question 12

Use the conversion formula   to replace the expression   by a sine function.

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Question 13

Starting with the identity   , choose the right trigonometric identity.

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Question 14

Sketch the curves without any technological help.   ;

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Question 15

Evaluate the integral

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Question 16

Use geometry to compute the given integral.

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Question 17

Evaluate the integral.

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Question 18

Evaluate the integral.

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Question 19

Use the addition formulas: sin ( x + y )= sin x cos y + cos x sin y sin ( x - y )= sin x cos y - cos x sin y cos ( x + y )= cos x cos y - sin x sin y cos ( x - y )= cos x cos y + sin x sin y to express   in terms of   .

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Question 20

Model the curve with a cosine function.   Note that the period of the curve is   and its range is   .

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Find the derivative of the function.

Evaluate the integral.

Find the derivative of the function.

Find the derivative of the function.

Recall that the average of a function on an interval is Calculate the 2-unit moving average of the function.

Evaluate the integral.

Model the curve with a sine function. Note that the period of the curve is and its range is 2.2, 2.2 and the graph of the sine function is shifted to the left 0.9 units.

Model the curve with a sine function. Note that the period of the curve is and its range is , the graph of the sine function is shifted to the right 3 units.

Model the curve with a cosine function. Note that the period of the curve is , its range is and the graph of the cosine function is shifted upward 65 units and shifted to the right 9 units. Write the model function as a function of (x)and .

Use the conversion formula to replace the expression by a sine function.

Starting with the identity , choose the right trigonometric identity.

Sketch the curves without any technological help. ;

Evaluate the integral

Use geometry to compute the given integral.

Evaluate the integral.

Evaluate the integral.

Use the addition formulas: sin ( x + y )= sin x cos y + cos x sin y sin ( x - y )= sin x cos y - cos x sin y cos ( x + y )= cos x cos y - sin x sin y cos ( x - y )= cos x cos y + sin x sin y to express in terms of .

Model the curve with a cosine function. Note that the period of the curve is and its range is .

Functions and Linear Models

Nonlinear Functions and Models

Introduction to the Derivative

Techniques of Differentiation With Applications

Further Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

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Exam 9: Trigonometric Models

Find the derivative of the function.

Evaluate the integral.

Find the derivative of the function.

Find the derivative of the function.

Recall that the average of a function on an interval is Calculate the 2-unit moving average of the function.

Evaluate the integral.

Model the curve with a sine function. Note that the period of the curve is and its range is 2.2, 2.2 and the graph of the sine function is shifted to the left 0.9 units.

Model the curve with a sine function. Note that the period of the curve is and its range is , the graph of the sine function is shifted to the right 3 units.

Model the curve with a cosine function. Note that the period of the curve is , its range is and the graph of the cosine function is shifted upward 65 units and shifted to the right 9 units. Write the model function as a function of (x)and .

Use the conversion formula to replace the expression by a sine function.

Starting with the identity , choose the right trigonometric identity.

Sketch the curves without any technological help. ;

Evaluate the integral

Use geometry to compute the given integral.

Evaluate the integral.

Evaluate the integral.

Use the addition formulas: sin ( x + y )= sin x cos y + cos x sin y sin ( x - y )= sin x cos y - cos x sin y cos ( x + y )= cos x cos y - sin x sin y cos ( x - y )= cos x cos y + sin x sin y to express in terms of .

Model the curve with a cosine function. Note that the period of the curve is and its range is .

Functions and Linear Models

Nonlinear Functions and Models

Introduction to the Derivative

Techniques of Differentiation With Applications

Further Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Filters