Calculus Answers

dS dt
=1000r 100 e(r/100)
The rate of change of the value of an investment, S, with respect to time, t ≥ 0, is given by
where r is the annual interest rate (assumed constant) and the principal of the investment is S(0) = 1 000
1.(a) Find an expression for S(t), that is, the value of the investment at time t.

A spring of natural lengthb19inches stretches 1.5 inches under a weight of pounds .find the work done in stretching the spring

A round pizza is baking in the oven. As the pizza gets warmer, its radius increases at a rate of 0.01 centimeters per minute. When the diameter of the pizza is 50 centimeters, what is the rate that the pizza's area is increasing?
Your solution myst include a sketch of the situation and labeling all given quantities. Leave your final answer in terms of pi.

A spring of natural length 10 inches stretches 1.5 inches under a
weight of 8 pounds. Find the work done in stretching the spring.
(a) from its natural length to a length of 14 inches
(b) from a length of 11 inches to a length of 13 inches.

The vector field F(x,y,z)=⟨2ze^(xy),xy^2z,sin(x+y)cos(z)⟩

is continuous on
Select one:
a. only the point (0,0)
.
b. all of R^2
.

c. all of R^3
.
d. all of R
.

What is the approximate area of the curve y = -e ^ (- 4x) between the x axis in the range (0, + ∞) ?

The rate of change of the value of investment, S , with respect to time, t>= 0, given by dS/dt = 2000(r/100)e^(rt/100).Where r is the annual interest rate (assumed constant) and the principal of the investment is S(0) = 2 000. (i)Find an expression for S(t), that is, the value of the investment at time t. (ii) Verify that your expression for S(t) is correct by computing S'(t).

The vector field F(x,y,z)=⟨2ze^(xy),xy^2z,sin(x+y)cos(z)⟩

is continuous on
Select one:
a. only the point (0,0)
.
b. all of R^2
.

c. all of R^3
.
d. all of R
.

Consider the scalar-valued function f(x,y)=√(8y+1), and the curve C described by y=2x^2 for x∈[0,1]. The value of ∫C f(x,y)ds

is
Select one:
a. 16
b. 8
c. 19/3
d. 16/3
e. 3/32
f. 32

If all the assumptions in Green's Theorem are satisfied, which of the following statements is true about Green's Theorem?
Select one:
a. The result in Green's Theorem provides a relationship between line integrals and conservative vector fields.
b. The result in Green's Theorem provides a relationship between line integrals and gradient vector fields.
c. The result in Green's Theorem provides a relationship between line integrals and double integrals.
d. The result in Green's Theorem provides a relationship between line integrals and triple integrals.