Calculus Answers

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 + 16
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?

Can x2+y2 sin(x)/x+y be made continuous by suitably defining it at (0; 0)?

if f(x,y) = 4x^3 - 3y^2, find fx

if (x,y) =x^2y^3 - 2y^-2, find fy

suppose f(x,y) = sin^2xcosy + xy^2, what is df/dx ?

Consider the following quadratic function.
f(x) = 2x2 − 4x − 1

Find the x- and y-intercepts of the graph, if any exist. (If an answer does not exist, enter DNE.)
x-intercept
(x, y) =



(smaller x-value)
x-intercept
(x, y) =



(larger x-value)
y-intercept
(x, y) =


Convert the function into standard form.
f(x) =


Identify the vertex and give an equation for the axis of symmetry.
vertex
(x, y) =



axis of symmetry

Find the radius of convergence and interval of convergence
of the series.
1. Sum of ((-1)^n)(x^n)/((1/n)^3) with n=1 -> infinite
2. Sum of ((-1)^n)(x^n)/(n^2) with n=1 -> infinite
3. Sum of (n^n)(x^n) with n=1 -> infinite
4. Sum of ((2x-1)^n)/(5(1/n)^n) with n=1 -> infinite

Determine whether the series is absolutely convergent,
conditionally convergent, or divergent.
1. Sum of (-1)^(n-1)(n)/(n^2+4) with n=1 -> infinite
2. Sum of (n!)/(100^n) with n=1 -> infinite
3. Sum of (n^10)/((-10)^(n+1)) with n=1 -> infinite
4. Sum of (3-cos(n))/(n^(2/3)-2) with n=1 -> infinite

Test the series for convergence or divergence
1. Sum of (-1)^(n-1)/(ln(n+4)) with n=1 -> infinite
2. Sum of (-1)^n.n/(sqrt(n^3+2)) with n=1 -> infinite
3. Sum of (-1)^n.sqrt(n)/(2n+3) with n=1 -> infinite
4. Sum of ncos(npi)/(2^n) with n=1 -> infinite

Determine whether the series converges or diverges
1. Sum of (2k-1)(k^2-1)/(k+1)((k^2+4)^2) with k=1 -> infinite
2. Sum of sqrt(n)/(n-1) with n=2 -> infinite
3. Sum of 1/(2n+3) with n=1 -> infinite
4. Sum of (n+2)/((n+1)^3) with n=3 -> infinite