Note: You may need to assume the fact that lim Me-M = 0 for all n. M +00 Decide whether or not the given integral converges. +0 x2e dx The integral converges. The integral diverges. If the integral converges, compute its value. (If the integral diverges, enter DNE.)

Q: Determine whether it converges or diverges. You must provide justification for your answer. sin(æ')…

A:

Q: 5 dx √√√5-x

A: Note:-Since you asked multiple questions according to our policy we can answer only first question…

Q: Evaluate the improper integral if it converges. (If the quantity diverges, enter DIVERGES.) -1 8 dx…

A:

Q: If the integral converges, enter its value. If the integral diverges, enter "diverges" (without the…

A:

Q: Determine if the integral converges or diverges by comparison.

A:

Q: Use the Integral Comparison Test to show that dx diverges by comparing with the integral Vr +1 1 dx;…

A: Integral comparison test:  Let fx and gx are continuous function for x≥a and fx≥gx≥0 for every x≥a.…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.