Calculus Answers

One earthquake has MMS magnitude 4.4. If a second earthquake has 730 times as much energy (earth movement) as the first, find the magnitude of the second quake.

Use spherical coordinates to find the volume of a solid that lies above the xy-plane, outside the sphere x²+y²+z²=2z and inside the sphere x²+y²+z²=4

• a) Sketch the region bounded by the graphs of the functions

                x²=x+1,   and    x= x²+4x+1.

• b) Determine the points of intersection of the curves given in part (a).
• c) Decide the limits of integration by using parts (a) and (b) and compute the area of the region that is bounded inside the graphs of both the curves. 

1. Eliminate a, b and c from, z=ax+by+cxy

2. Eliminate a & b from az+b=a²x+y

3. Solve z(x-y)=x²p-y²q

3. Solve 2p+3q=1

find the area of the region bounded by the lines y=x y=3x and x+y=4 using double integral

Use double integrals and polar coordinates to find the volume of the solid that lies inside the graph of both x²+y²=1 and x²+y²+z²=9

The base of an isosceles triangle is 8 feet long. If the altitude is 6 feet long and increasing 3 inches per minute, at what rate are the base angles changing?

The base diameter and altitude of a right circular cone are observed at a certain instant to be 10 and 20 inches, respectively. If the lateral area is constant and the base diameter is increasing at a rate of 1 inch per minute, find the rate at which the altitude is decreasing.

Let f be the function given by f(x)=x/(x-4)(x+2) on the closed interval [-7,7]. Of the following intervals, on which can the Mean Value Theorem be applied?

I. [-1,3] because f is continuous on [-1,3] and differentiable (-1,3)

II. [5,7] because f is continuous on [5,7] and differentiable (5,7)

III. [1,5] because f is continuous on [1,5] and differentiable (1,5)

A. None

B. I only

C. I and II only

D. I, II, and III

Let f be a differentiable function with f(0)=-4 and f(10)=11. which of the following must be true for some c in the interval (0,10)?

A) f'(c)=0, since the Extreme Value Theorem applies

B) f'(c)=11+(-4)/10-0 since the Mean Value Theorem applies

C) f'(c)=11-(-4)/10-0, since the Mean Value Theorem applies

D) f'(c)=1.5, since the Intermediate Value Theorem applies