Calculus Answers

A)The rate of change of the value of an investment ,S, with respect to time, t>= 0, is given by ds/dt= 1000(r/10)^e^rt/100 Where r is the annual interest rate (assumed constant) and the principal of the investment S(0)=10 000 1. Find an expression for S(t), that is, the value of the investment at time t. 2. Verify that your expression for S(t) is correct by computing S'(t) 3. Explain why S(t) is continuous for t>=O
4..How long would it take for the investment to be exactly 15 000

Determine the area of the region bounded by f(x) = 2x
2 + 10 and g(x) = 4x + 1

d) Media consultants for the new local magazine IT-Solutions! have projected that the number of subscriptions will grow during the first five years at a rate given by [5 Marks]
S
0
(t) = 1000
(1 + 0.3t)
3/2
, 0 ≤ t ≤ 60
where t is the number of months since the magazine’s first issue and S
0
(t) is the rate of change in the
number of subscriptions measured in subscriptions/month. Evaluate and interpret Z 6
0
S
0
(t) d

A)Find the area bounded by the curve y=|x-1|, the axis and the lines x=7 and x=11
B)The rate of change of the value of an investment ,S, with respect to time, t>= 0, is given by ds/dt= 1000(r/10)^e^rt/100
Where r is the annual interest rate (assumed constant) and the principal of the investment S(0)=10 000
1. Find an expression for S(t), that is, the value of the investment at time t.
2. Verify that your expression for S(t) is correct by computing S'(t)
3. Explain why S(t) is continuous for t>=O
4. Determine by computing lim t ~ ○○( positive infinity) S(t) , what would happen to the value of the investment if t were to grow without bound. Intrepret the result.
5.How long would it take for the investment to be exactly 15 000.

Let c,r be constants, and D={(x,y,z):x^2+y^2+z^2≤r^2}. The answer to ∭D cdV

is
Select one:
a. (π^2cr^3)/3


b. (4πcr^3)/3

c. 4πcr^3

d. (πcr^4)/3


e. (4πcr^2)/2

f. (4r^3)/3


g. (πcr^3)/3

Let c,r be constants, and D={(x,y,z):x^2+y^2+z^2≤r^2}. The answer to ∭D cdV

is
Select one:
a. (π^2cr^3)/3


b. (4πcr^3)/3

c. 4πcr^3

d. (πcr^4)/3


e. (4πcr^2)/2

f. (4r^3)/3


g. (πcr^3)/3

Let c,r be constants, and D={(x,y,z):x^2+y^2+z^2≤r^2}. The answer to ∭D cdV

is
Select one:
a. (π^2cr^3)/3


b. (4πcr^3)/3

c. 4πcr^3

d. (πcr^4)/3


e. (4πcr^2)/2

f. (4r^3)/3


g. (πcr^3)/3

Let c,r be constants, and D={(x,y,z):x^2+y^2+z^2≤r^2}. The answer to ∭D cdV

is
Select one:
a. (π^2cr^3)/3


b. (4πcr^3)/3

c. 4πcr^3

d. (πcr^4)/3


e. (4πcr^2)/2

f. (4r^3)/3


g. (πcr^3)/3

Given the function f(x) = 2xsquared - x-1
(f) List the y - intercepts, if there is any, of the graph of f .
(g) Find all point(s) at which f'(x) =0?
(h) Determine the intervals on which the graph of f (x) is increasing and the intervals on which
it is decreasing.
(i) Use the First Derivative Test to identify the maximum and/or minimum point(s) of f (x) .
(j) Use the Second Derivative Test to determine the nature of concavity of f (x) .

Given the function f(x) =2xsquared - x-1
(a) Is the point (-1, 2) on the graph of f .
(b) If x=-2, what is f(x) ? What point is on the graph of f ?
(c) If f (x)=-1, what is x ? What point(s) are on the graph of f ?
(d) What is the domain of f ?
(e) List the x - intercepts, if any, of the graph of f .