Questions from General Calculus

Q: Test the series for convergence or divergence. /

Test the series for convergence or divergence.

Q: Find the sum of the series. /

Find the sum of the series.

Q: Evaluate the integral. /

Evaluate the integral.

Q: A rocket accelerates by burning its onboard fuel, so its mass

A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel is consumed at rate r, and the...

Q: Express the repeating decimal 4.17326326326... as a fraction.

Express the repeating decimal 4.17326326326... as a fraction.

Q: Evaluate the integral. /

Evaluate the integral.

Q: Use the Root Test to determine whether the series is convergent or

Use the Root Test to determine whether the series is convergent or divergent.

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 integration by parts to prove the reduction formula. /

Use integration by parts to prove the reduction formula.

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...