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Mass of a wire In Exercises 1–6, find the mass M and center of mass x of the linear wire covering the given interval and having the given density 8(x). 1. 1< xS 4, 8(x) = Vx 2. -3 < x < 3, 8(x) = 1 + 3x² 3. 0 < x< 3, 8(x) = 4. 1< x< 2, 8(x) x3 = S4, 0

Verify the integration formulas in Exercises 37–40.
sech x dx = tan'(sinh x) + C
37. a.
sech x dx = ...

Find the area bounded by Y1=X2, Y2=X, X=0 and X=2 graph it and show ALL

45. The cubical metal tank shown here has a parabolic gate held in
place by bolts and designed to wi...

From the graph of f, state each x-value at which f is discontinuous. For each x-value, determine whe...

The percentage of people of any particular age group that will die in a given year may be approximat...

Water is pumped into a sphere of radius R at a variable rate in such a way that the water level rise...

2.) (3x + x2) sin(2x) dx Use whatever method you want to

Tutorial Exercise
Use the given transformation to evaluate the given integral, where R is the triang...

Find the exact length of the curve.

y = (x-x2)1/2 + sin-1((x1/2))

find
3 sec“ 3x dx
sec4 0 do
41.
42.
csc“ 0 do
secó x dx
43.
44.
7/4
4 tan³ x dx
6 tan“ x dx
45.
46.
...

Find the derivative of f (x) = 2e".
f' (æ) =

Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and th...

use the theorums on derivatives to find the derivative of the following function:

f​(x) = (7"StartR...

What values of a and b minimize the value of
- 2x?) dx?
(x*

For this problem, fill in each blank with the correct answer.
Syntax example: to enter r? sin (), ty...

Find the length of the arc of the curve from point P to point Q.

x2 = (y − 8)3,  P(1, 9),  Q(8, 12)

APPlicationS
32. The length of one arch of the curve y = sin x is given by
V1 + cos² x dx.
L =
Estim...

Show that the following statement is false by drawing a graph that provides a counterexample: If f i...

112. True, sometimes true, or never true? The area of the region be-
tween the graphs of the continu...

64. What is the largest value
| xV2r - x° dx
can have for ny a and b? Give reasons for your answer.

State whether f (2) and f (4) are local minima or local maxima, assuming that Figure 14 is the graph...

52. Use the substitution u = tan x to evaluate the integral
dx
1+ sin? x

67. Proof of the Second Derivative Test Let c be a critical point such that f"(c) > 0 [the case f"(c...

A round underwater transmission cable consists of a core of
copper wires surrounded by nonconducting...

Suppose that f (0) = 2 and f' (x) ≤ 3 for x &gt; 0. Apply the MVT to the interval [0, 4] to prove th...

25. Find the angle 0 that maximizes the area of the isosceles triangle whose legs have length e (Fig...

If f is concave up, then f' is (choose one): (a) increasing. (b) decreasing.

For this problem, we want to integrate f (x) = (x − 2)/(x^2 + 4). 



5c please!

b. Differentiate both sides of the equation in part (a) with re-
86. The hyperbolic in hyperbolic fu...

Find two positive real numbers such that the sum of the first number squared and the second number i...

T 69. Which is bigger, 7 or e™? Calculators have taken some of
the mystery out of this once-challeng...

In Exercises 27–40, use a substitution to change the integral into one
you can find in the table. Th...

where m, n
Evaluate lim
X/2 cos nx
+0 are integers.

Consider the function f(x), for which f(0) = 7 and f'(0) = 9
find h'0 for the function h(x) = 1/f(x)

42. Whatever the value of p > 0 in the equation y = x²/(4p), the
y-coordinate of the centroid of the...

Determine the sign combinations of f' and f" for each interval A-G in Figure 16.
y=f(r)
А всD EF
FIG...

16. (Continuation of Exercise
15.) Show that the
value of
In (x + a)
lim
In x
is the same no matter ...

18. The graph of x2/3 + y²/3 = 1 is called an astroid and is given be-
low. Find the volume of the s...

evaluate the limit if it exists. If not, determine whether the one-sided limits exist (finite or inf...

1/10
1.A) e* cos(5x) dx integration by parts

E. The error function
The error function,
2
erf (x) =
et dt,
important in probability and in the the...

Are all sign transition possible? Explain with a sketch why the transitions ++ → −+ and −− → +− do n...

4. Which of the following functions grow faster than x2 as x→∞?
Which grow at the same rate as x²? W...

Mass of a wireIn Exercises 1–6, find the mass M and center of mass x of the linearwire covering the given interval and having the given density 8(x).1. 1< xS 4, 8(x) = Vx2. -3 < x < 3, 8(x) = 1 + 3x²3. 0 < x< 3, 8(x) =4. 1< x< 2,8(x)x3=S4, 0

1) Find the mass and center of mass of following function:
<img src="https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/690b93c1-a36f-4ba6-8aab-a0d4b7e86b05/f46cf055-8b1d-49e5-8b62-9d540b500221/ujippgn.png" alt="Calculus homework question answer, step 1, image 1" />
<img src="https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/690b93c1-a36f-4ba6-8aab-a0d4b7e86b05/f46cf055-8b1d-49e5-8b62-9d540b500221/618os59.png" alt="Calculus homework question answer, step 1, image 2" />

2) Find the mass and center of mass of following function:
<img src="https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/690b93c1-a36f-4ba6-8aab-a0d4b7e86b05/f46cf055-8b1d-49e5-8b62-9d540b500221/5zbcyll.png" alt="Calculus homework question answer, step 2, image 1" />
<img src="https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/690b93c1-a36f-4ba6-8aab-a0d4b7e86b05/f46cf055-8b1d-49e5-8b62-9d540b500221/o7tva3.png" alt="Calculus homework question answer, step 2, image 2" />...

Mass of a wire In Exercises 1–6, find the mass M and center of mass x of the linear wire covering the given interval and having the given density 8(x). 1. 1< xS 4, 8(x) = Vx 2. -3 < x < 3, 8(x) = 1 + 3x² 3. 0 < x< 3, 8(x) = 4. 1< x< 2, 8(x) x3 = S4, 0

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Mass of a wire In Exercises 1–6, find the mass M and center of mass x of the linear wire covering the given interval and having the given density 8(x). 1. 1< xS 4, 8(x) = Vx 2. -3 < x < 3, 8(x) = 1 + 3x² 3. 0 < x< 3, 8(x) = 4. 1< x< 2, 8(x) x3 = S4, 0

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