Questions from General Calculus


Q: Use a Riemann sum with n = 4 and left endpoints to

Use a Riemann sum with n = 4 and left endpoints to estimate the area under the graph in Fig. 1 for 0 ≤ x ≤ 2. Figure 1:

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Q: Redo Exercise 47 using right endpoints. Exercise 47:

Redo Exercise 47 using right endpoints. Exercise 47: Use a Riemann sum with n = 4 and left endpoints to estimate the area under the graph in Fig. 1 for 0 ≤ x ≤...

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Q: Use a Riemann sum with n = 2 and midpoints to estimate

Use a Riemann sum with n = 2 and midpoints to estimate the area under the graph of f (x) = 1/(x + 2) on the interval 0 ≤ x ≤ 2. Then, use a definite integral to find the exact value of the area to f...

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Q: Use a Riemann sum with n = 5 and midpoints to estimate

Use a Riemann sum with n = 5 and midpoints to estimate the area under the graph of f (x) = e2x on the interval 0 ≤ x ≤ 1. Then, use a definite integral to find the exact value of the area to five deci...

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Q: Find the consumers’ surplus for the demand curve p = √(25

Find the consumers’ surplus for the demand curve p = √(25 - .04x) at the sales level x = 400.

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Q: Three thousand dollars is deposited in the bank at 4% interest

Three thousand dollars is deposited in the bank at 4% interest compounded continuously. What will be the average value of the money in the account during the next 10 years?

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Q: Find the average value of f (x) = 1/

Find the average value of f (x) = 1/x3 from x = 1/3 to x = 1/2.

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

Find the value of k that makes the antidifferentiation formula true. ∫7/(8 - x)4 dx = k/(8 - x)3 + C

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Q: Suppose that the interval 0 ≤ x ≤ 1 is divided into

Suppose that the interval 0 ≤ x ≤ 1 is divided into 100 subintervals with a width of Δx = .01. Show that the sum [3e-0.01] Δx + [3e-0.02] Δx + [3e-0.03] Δx + … + [3e-1] Δx is close to 3(1 - e-1).

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Q: In Fig. 2, three regions are labeled with their areas

In Fig. 2, three regions are labeled with their areas. Determine a∫c f (x) dx and determine a∫d f (x) dx. Figure 2:

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