Reference no: EM133050795

Question 1: Evaluate the line integral, where C is the given curve.

∫_c xdx + 2y√xdy, where C is the arc of the parabola x = -y² + 1 from (1,0) to (0,1).

Question 2:

Sum from n=0 to inf (2^(2n+1)/3^(2n+1)) =
a. 8/15
b. 6/5
c. None
d. 2/3
e. Diverges

Question 3:

Find the curvature.

r(t) =  8ti + sin(t)j + 5 cos(t)k

k(t) = (No Response)

Question 4:

What is the rate of change of the perimeter when the length is 5 inches?

The length of a rectangle is being lengthened at the rate of 2 inches per second while the width is shortened in such a way that the figure remains a rectangle with a constant area of SO square inches. What is the rate of change of the perimeter when the length is 5 inches?

a. -4 in/sec

b. 8 in/sec

c. 4 in/sec

d. -8 in/sec

Question 5:
Sumi Kato's savings account has a balance of $1,568. After 6 years what will the amount of interest be at 5.5% compounded annually? Round to the nearest cent.

Select one:
$2162.025
$594.025
$583.277
$940.805

Question 6:

Consider the function f(x) = 4x³ - 6x on the interval [ - 4, 4]. Find the average or mean slope of the function on this interval.

By the Mean Value Theorem, we know there exists at least one c in the open interval ( - 4, 4) such that f ' (c) is equal to this mean slope.

For this problem, there are two values of c that work.

The smaller one is

and the larger one is

Question 7:

It must be stated and shown if the series converges or diverges.

_n=5∑^∞ (-0.99)ⁿ⁺¹