Questions from General Calculus

Q: Determine whether the sequence is increasing, decreasing, or not monotonic

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

Q: Find the value of c if ∑∞n-2 (1

Find the value of c if ∑∞n-2 (1 + c)-n = 2

Q: The function j1 defined by is called the Bessel function of order

The function j1 defined by is called the Bessel function of order 1. (a). Find its domain. (b). Graph the first several partial sums on a common screen. (c). If your CAS has built-in Bessel function...

Q: Find the value of c such that ∑∞n=0 enc

Find the value of c such that ∑∞n=0 enc = 10

Q: In Example 7 we showed that the harmonic series is divergent.

In Example 7 we showed that the harmonic series is divergent. Here we outline another method, making use of the fact that ex > 1 + x for any x > 0. (See Exercise 4.3.62.) If sn is the nth partial sum...

Q: We know that lim n→∞ (0.8)n

We know that lim n→∞ (0.8)n = 0 [from (7) with r = 0.8]. Use logarithms to determine how large has to be so that (0.8)n < 0.000001.

Q: What is wrong with the following calculation? (Guido Ubaldus

What is wrong with the following calculation? (Guido Ubaldus thought that this proved the existence of God because “something has been created out of nothing.”)

Q: Suppose that ∑∞n-1 an (an ≠ 0)

Suppose that ∑∞n-1 an (an ≠ 0) is known to be a convergent series. Prove ∑∞n-1 1/an that is a divergent series.

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

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