Questions from General Calculus

Q: Use the Table of Integrals on Reference Pages 6–10 to

Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral.

Q: Determine whether the geometric series is convergent or divergent. If it

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.

Q: Find the Maclaurin series for f and its radius of convergence.

Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the...

Q: Use Simpson’s Rule with n = 6 to estimate the area under

Use Simpson’s Rule with n = 6 to estimate the area under the curve y = ex/x from x = 1 to x = 4.

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

Q: A particle that moves along a straight line has velocity v(

A particle that moves along a straight line has velocity v(t) − t2e2t meters per second after t seconds. How far will it travel during the first t seconds?

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

Q: (a) What is an alternating series? (b

(a) What is an alternating series? (b) Under what conditions does an alternating series converge? (c) If these conditions are satisfied, what can you say about the remainder after n terms?

Q: Prove part (i) of Theorem 8.

Prove part (i) of Theorem 8.

Q: Test the series for convergence or divergence. /

Test the series for convergence or divergence.