Current Score : 33 / 33 Due : Friday, March 21 2014 11:59 PM EDT

1. 1/1 points | Previous Answers SCalcET7 3.3.001.

Differentiate.

2. 1/1 points | Previous Answers SCalcET7 3.3.002.

Differentiate.

f '(x) =

3. 1/1 points | Previous Answers SCalcET7 3.3.003.

Differentiate.

Section 3.3 HW (Homework)Frances CoronelMAT 151 Calculus I, Spring 2014, section 01, Spring 2014Instructor: Ira Walker

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f(x) = 6x6 − 5 cos x

f '(x) =

f(x) = 4 sin xx

f(x) = sin x + cot x19

f '(x) =

4. 1/1 points | Previous Answers SCalcET7 3.3.005.

Differentiate.

y' =

5. 1/1 points | Previous Answers SCalcET7 3.3.007.

Differentiate with respect to t.

6. 1/1 points | Previous Answers SCalcET7 3.3.009.MI.

Differentiate.

y' = Master ItDifferentiate.

Part 1 of 2

The function is a quotient, so we'll need to use the Quotient Rule, which states that

Recall that the derivative of cot x is (No Response) . (It's important to simply memorize the derivatives of all six trigonometricfunctions.)

y = sec θ tan θ

y = a cos t + t2 sin t

y' =

y = 6x7 − cot x

y = 3x8 − cot x

y = 3x8 − cot x

= .ddx

f(x)g(x)

g(x)f '(x) − f(x)g'(x)(g(x))2

7. 2/2 points | Previous Answers SCalcET7 3.3.009.MI.SA.

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive anypoints for the skipped part, and you will not be able to come back to the skipped part.

Tutorial ExerciseDifferentiate.

Part 1 of 2

The function is a quotient, so we'll need to use the Quotient Rule, which states that

Recall that the derivative of tan x is . (It's important to simply memorize the derivatives of all sixtrigonometric functions.)

Part 2 of 2Now, applying the Quotient Rule, we conclude that the derivative is as follows.

You have now completed the Master It.

8. 1/1 points | Previous Answers SCalcET7 3.3.011.

Differentiate.

y = 7x6 − tan x

y = 7x6 − tan x

= .ddx

f(x)g(x)

g(x)f '(x) − f(x)g'(x)(g(x))2

y' =

f(θ) = sec θ1 + sec θ

f '(θ) =

9. 1/1 points | Previous Answers SCalcET7 3.3.015.

Differentiate.

f '(x) =

10.5/5 points | Previous Answers SCalcET7 3.3.017.

Prove that

11.1/1 points | Previous Answers SCalcET7 3.3.021.

Find an equation of the tangent line to the curve at the given point.

y =

f(x) = 8xex csc x

(csc x) = −csc x cot x.ddx

(csc x) =

=

=

= − ·

= −csc x cot x

ddx

ddx

1

(0) − 1

sin2 x

sin2 x

1sin x

sin x

y = sec x, (π/3, 2)

12.2/2 points | Previous Answers SCalcET7 3.3.025.

(a) Find an equation of the tangent line to the curve at the point (π/2, 2π).

y =

(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.

13.2/2 points | Previous Answers SCalcET7 3.3.028.

If

y = 4x sin x

f(x) = 9ex cos x, find f '(x) and f ''(x).

f '(x) =

f ''(x) =

14.3/3 points | Previous Answers SCalcET7 3.3.031.

(a) Use the Quotient Rule to differentiate the function

(b) Simplify the expression for by writing it in terms of sin x and cos x, and then find

(c) Are your answers to parts (a) and (b) equivalent?

15.2/2 points | Previous Answers SCalcET7 3.3.032.

Suppose and let and Find the following.

(a)

(b)

f(x) = .tan x − 1sec x

f '(x) =

f(x) f '(x).

f '(x) =

Yes

No

f(π/3) = 5 and f '(π/3) = −7, g(x) = f(x) sin x h(x) = (cos x)/f(x).

g'(π/3)

h'(π/3)

16.1/1 points | Previous Answers SCalcET7 3.3.033.

For what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable. Enter your answers as acomma-separated list.)

x =

17.7/7 points | Previous Answers SCalcET7 3.3.035.MI.

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is where t is in seconds and x is in centimeters.

(a) Find the velocity and acceleration at time t.

Master ItA mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is

where t is in seconds and x is in centimeters.

Find the velocity and acceleration at time t.Part 1 of 2If the equation of motion is given by then the velocity is given by (No Response) and the acceleration is given by(No Response) .

(b) Find the position, velocity, and acceleration of the mass at time t = 2π/3.

=

=

f(x) = x + 2 sin x

x(t) = 8 sin t,

v(t) =

a(t) =

x(t) = 6 cos t,

f(t),

x 2π3

v 2π3

=

In what direction is it moving at that time?

Since < 0, the particle is moving to the left .

Master ItA mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is

where t is in seconds and x is in centimeters.

Find the position, velocity, and acceleration of the mass at time t = π/6. In what direction is it moving at that time?Part 1 of 4

At time the position is given by the following.

a 2π3

v 2π3

x(t) = 6 cos t,

t = ,π6

x(t) = 6 cos t

x = 6 cos

= 6

= (No Response)

π6

π6

(No Response)2