Calculus Answers

Use Green’s theorem, and apply it to evaluate ∫(3x^2–4y)dx–(2x+y^3)dy where C is the ellipse 4x^2+9y^2=25

Using Lagrange Obtain the dimensions of a box of maximum volume that can be inscribed in a ellipsoid x²/a²+y²/b²+z²/c²=1

Given Z=f(x-2y)+g(3x+y) such that Zxx + AZxy+BZyy=0 Find A and B

Please how do we distinguish or know when it is a minimum or maximum or saddle point in an extrema of two or more variables(multivariable) function.

Y = 2^3x + 1/2 ln x + 4 t^3

Y = 3e^2x + 4 sin x

∫∫∫cos(x^2+y^2+z^2)^(3/2) dxdydz

s the graph of y = sin(x

5

) increasing or decreasing when

x = 12? (enter increasing, decreasing, or neither).

Is it concave up or concave down? (enter up, down,

or neither).

1. Find the general term of the sequence, starting with n=1, determine whether the sequence converges, and if so find its limit.

9/10, 9/20, 29/30, 39/40 ...

2. Find the general term of the sequence, starting with n=1 determine whether the sequence converges, and if so find its limit. The general term of the sequence is bracket a sub n bracket, positive where n=1.

19, 19/7, 19/ 49, 19/343 ...

3. Starting n=1, and considering the even and odd terms separately, find a formula for the general term of the sequence

1, 1/81, 3, 1/9^4, 5, 1/9^6 ...

4. Consider the sequence

a1 = 90^1 /2
a2 = 90^ 1/2 + 90^1/4
a3 = 90^1/2 +90^1/4 +90^1/8

A. find the recursion formula for a sub n+1.
B. Assuming that the sequence converges, find its limit L

1. Write out the first five terms of the sequence, determine whether the sequence converges, and if so find its limit.

positive infinity
bracket n / n+7 bracket
n=1


2. Write out the first five terms of the sequence, determine whether the sequence converges, and if so find its limit.

positive infinity
bracket 5+(-1)^n 5 bracket
n=1

3. Write out the first five terms of the sequence, determine whether the sequence converges, and if so find its limit.

positive infinity
bracket n / 2^n bracket
n=1


4. Write out the first five terms of the sequence, determine whether the sequence converges, and if so find its limit

positive infinity
bracket (n+1)(n+5) / 2(n^2)
n=1