Calculus Answers

Determine whether the series is convergent or divergent
1. 1+1/2.sqrt(2) +1/3.sqrt(3) +1/4.sqrt(4) +...
2. Sum of n^2/(n^3+1) with n=1 -> infinite
3. Sum of (3n-4)/(n^2-2n) with n=3 -> infinite
4. Sum of 1/(n^2 +6n+13) with n=1 -> infinite

1.Calculate the first eight terms of the sequence of partial
sums correct to four decimal places. Does it appear that the series
is convergent or divergent?
Sum of ((-1)^(n-1))/(n!) with n=1 -> infinite
2.Determine whether the geometric series is convergent or
divergent. If it is convergent, find its sum.
a) 4+3+9/4+27/16+...
b) Sum of (1)/((sqrt(2))^n) with n=0 -> infinite
c) Sum of (e^n)/(3^(n-1)) with n=1 -> infinite

Determine whether the sequence converges or diverges.
If it converges, find the limit:
1. a(n) = (n^3)/(n+1)
2. a(n) = sqrt((n+1)/(9n+1))
3. a(n) = ((-1)^(n+1).n)/(n+sqrt(n))
4 a(n) = cos(n/2)

if f(x,y) = x^3 y^2 - sin^2 x cos2y, what is df/dy

if f(x,y) = tan ^-1 y/x, find fx

Sketch the following relation.
R = {(x, y) : y ≤ x − 2}


Sketch the following relation.
R = {(x, y) : x2 ≤ y < x + 6}

What is the largest rectangular area one can enclose with 38 inches of string?
______ in2

The original function used to model the cost of producing x PortaBoys Game Systems was
C(x) = 80x + 150.
While developing their newest game, Sasquatch Attack!, the makers of the PortaBoy revised their cost function using a cubic polynomial. The new cost of producing x PortaBoys is given by
C(x) = .03x3 − 4.5x2 + 229x + 250.
Market research indicates that the demand function
p(x) = −1.5x + 250
remains unchanged. Find the production level x that maximizes the profit made by producing and selling x PortaBoys. (Round your answer to the nearest whole number.)
x =________ PortaBoys

The International Silver Strings Submarine Band holds a bake sale each year to fund their trip to the National Sasquatch Convention. It has been determined that the cost in dollars of baking x cookies is
C(x) = 0.5x + 23
and that the demand function for their cookies is
p = 14 − 0.05x.
How many cookies should they bake in order to maximize their profit?

1. (An Intermediate Algebra review exercise) Use polynomial long division to perform the indicated division. Write the polynomial in the form
p(x) = d(x)q(x) + r(x).
(9x4 − 3x3 + 2x2 − 9) ÷ (x2 + 4)
p(x) =

2.Use polynomial long division to perform the indicated division. Write the polynomial in the form
p(x) = d(x)q(x) + r(x).
(−x5 + 8x3 − x) ÷ (x3 − x2 + 8)
p(x) =

3. For the polynomial given below, you are given one of its zeros. Use the techniques in this section to find the rest of the real zeros. (Enter your answers as a comma-separated list.)
x3 − 6x2 + 11x − 6, c = 1
x =

Factor the polynomial.


4.For the polynomial given below, you are given one of its zeros. Use the techniques in this section to find the rest of the real zeros. (Enter your answers as a comma-separated list.)
x3 − 12x2 + 48x − 64, c = 4
x =

Factor the polynomial.