section 3.3 hw
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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