Questions from Calculus

Q: Use the integral test to determine whether the infinite series is convergent

Use the integral test to determine whether the infinite series is convergent or divergent. (You may assume that the hypotheses of the integral test are satisfied.) ∑k=2∞ (k + 1)/(k2 + 2k + 1)2

Q: It can be shown that ∫0∞ 3/(9

It can be shown that ∫0∞ 3/(9 + x2) dx is convergent. Use this fact to show that an appropriate infinite series converges. Give the series, and show that the hypotheses of the integral test are satisf...

Q: Use the integral test to determine if a ∑k=1

Use the integral test to determine if a ∑k=1∞ e1/k k2 is convergent. Show that the hypotheses of the integral test are satisfied.

Q: It can be shown that lim b → ∞ be-b

It can be shown that lim b → ∞ be-b = 0. Use this fact and the integral test to show that a ∑k=1∞ k ek is convergent.

Q: Is the series a ∑k=1∞ 3k/4k

Is the series a ∑k=1∞ 3k/4k convergent? What is the easiest way to answer this question? Can you tell if ∫1∞3x/4x dx is convergent?

Q: Use the comparison test to determine whether the infinite series is convergent

Use the comparison test to determine whether the infinite series is convergent or divergent. ∑k=2∞ 1/(k2 + 5) [Compare with ∑k=2∞ 1/k2.]

Q: Use the comparison test to determine whether the infinite series is convergent

Use the comparison test to determine whether the infinite series is convergent or divergent. ∑k=2∞ 1/√(k2 – 1) [Compare with ∑k=2∞ 1/k.]

Q: Determine the fourth Taylor polynomial of ln x at x = 1

Determine the fourth Taylor polynomial of ln x at x = 1.

Q: Use the comparison test to determine whether the infinite series is convergent

Use the comparison test to determine whether the infinite series is convergent or divergent. ∑k=1∞ 1/(2k + k) [Compare with ∑k=1∞ 1/2k.]

Q: Use the comparison test to determine whether the infinite series is convergent

Use the comparison test to determine whether the infinite series is convergent or divergent. ∑k=1∞ 1/k3k [Compare with ∑k=1∞ 1/3k.]