This solution shows you step by step on how to solve calculus problems involving differentiation. In addtion, it shows you detailed steps on how to do differentiation from the first principles.

Please see the attached file for the fully formatted problems.
1. Use an iterated integral to find the area of a region...
2. Evaluate the double integral...
3. Use double integral to find the volume of a solid...
4. Verify moments of inertia...
5. Limit of double integral...
6. Surface area...
7. Triple integral...

This solution shows how to solve for various calculusproblems, including differentiation of functions using the product rule, the quotient rule, and the chain rule, as well as how to calculate integrals.

Using the Fundamental Theorem of Calculus I need to find the solution of the following problems. Can you explain how?
Please see the attached file for the fully formatted problems.

We have the function f(x,y) = e^(-x^2 + y^2) :
a. To draw some level curves;
b. Calculate the gradient and determine the stationary points;
c. To write the equation of the tangent plane to z = f(x,y) in the point (0, 0, f(0, 0)), and in the point A (1,1,f(1,1));
d. To write the Taylor formula of f(x,y) stopped to the 2nd ord

** Please see the attached file for the complete problem description **
14. f(x) = (x^3 + 2x+ 1) (2+ (1)/(x^2)) Find derivative
34. Suppose f and g are functions that are differentiable at x = 1 and that:
f(1) = 2
f prime (1) = -1
g(1) = -2
g prime (1) = 3
Find the Value of h prime (1) for : h(x

I need help with these two problems. If you could please explain the solution, I would appreciate it.
1.Use cylindrical shells to compute the volume. The region bounded by y = x and y = x2 - 2, revolved about x = 3
2. A solid is formed by revolving the given region about the given line. Compute the volume exactly if possi

Please help me with the following calculusproblems:
1) Set up (do not integrate) an integral for the length of the curve y=tan-1x for x E [0,π).
2) Find the surface area obtained by rotating the curve x=2-y2 around the y axis.
3) Find the centroid of the region bounded by the curve x=2-y2 and the y axis.

12) What is limit as h approaches 0 of [cos(pi/2 + h) - cos(pi/2)] / [h]
Ans is -1. Explain.
14) The area of the region in the first quadrant between the graph of y=x times the
sqrt of (4-x^2) and the x axis is? Ans is 8/3. Explain.
15) If x^2 + y^3 = x^3y^2, then dy/dx = ? Explain.
Ans is [3x^2y^2 - 2x]

Let p1 = (4,0,4), p2 = (2,-1,8), and p3 = (1,2,3).
a) Show that the three points define a right triangle. Hint the difference between two vertices is a vector whose direction coincides with that of a triangle side, and a pair of such vectors must be orthogonal in order for the triangle to be a right triangle.
b) Specify