Questions from General Calculus

Q: Find the volume of the solid of revolution generated by revolving about

Find the volume of the solid of revolution generated by revolving about the x-axis the region under the curve y = 1 - x2 from x = 0 to x = 1.

Q: A store has an inventory of Q units of a certain product

A store has an inventory of Q units of a certain product at time t = 0. The store sells the product at the steady rate of Q/A units per week and exhausts the inventory in A weeks. (a) Find a formula f...

Q: A retail store sells a certain product at the rate of g

A retail store sells a certain product at the rate of g(t) units per week at time t, where g(t) = rt. At time t = 0, the store has Q units of the product in inventory. (a) Find a formula f (t) for the...

Q: Let x be any positive number, and define g(x

Let x be any positive number, and define g(x) to be the number determined by the definite integral g(x) = 0∫x 1/(1 + t2) dt. (a) Give a geometric interpretation of the number g(3). (b) Find the deri...

Q: For each number x satisfying -1 … x … 1,

For each number x satisfying -1 … x … 1, define h(x) by h(x) = -1∫x √ (1 - t2) dt. (a) Give a geometric interpretation of the values h(0) and h(1). (b) Find the derivative h ‘(x).

Q: Suppose that the interval 0 ≤ t ≤ 3 is divided into

Suppose that the interval 0 ≤ t ≤ 3 is divided into 1000 subintervals of width Δt. Let t1, t2, … , t1000 denote the right endpoi...

Q: What number does [e0 + e1/n + e2

What number does [e0 + e1/n + e2/n + e3/n + … + e(n-1)/n] * 1/n approach as n gets very large?

Q: What number does the sum [13 + (1

What number does the sum [13 + (1 + 1/n)3 + (1 + 2/n)3+ (1 + 3/n)3+ … + (1 + n-1/n)3] * 1/n approach as n gets very large?

Q: Find the value of k that makes the antidifferentiation formula true.

Find the value of k that makes the antidifferentiation formula true. ∫ (3x + 2)4 dx = k(3x + 2)5 + C

Q: In Fig. 3, the rectangle has the same area as

In Fig. 3, the rectangle has the same area as the region under the graph of f (x). What is the average value of f (x) on the interval 2 ≤ x ≤ 6? Figure 3: