Questions from General Calculus

Q: Evaluate the integral. /

Evaluate the integral.

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

Determine whether the sequence is convergent or divergent. If it is convergent, find its limit.

Q: A sequence is defined recursively by the equations a1 = 1,

A sequence is defined recursively by the equations a1 = 1, an+1 = 1 3 (an +4). Show that {an} is increasing and an < 2 for all n. Deduce that / is convergent and find its limit.

Q: Evaluate the indefinite integral. Illustrate, and check that your answer

Evaluate the indefinite integral. Illustrate, and check that your answer is reasonable, by graphing both the function and its antiderivative (take C − 0).

Q: Determine whether the series is convergent or divergent. /

Determine whether the series is convergent or divergent.

Q: Determine whether the series is convergent or divergent. /

Determine whether the series is convergent or divergent.

Q: Determine whether the series is convergent or divergent. /

Determine whether the series is convergent or divergent.

Q: Determine whether the sequence converges or diverges. If it converges,

Determine whether the sequence converges or diverges. If it converges, find the limit.

Q: Evaluate the integral. /

Evaluate the integral.

Q: Determine whether the series is convergent or divergent. /

Determine whether the series is convergent or divergent.