LM 7.8: Improper Integrals

Question 1

For a type 1 improper integral (0 to infinity or -infinity to 0), when will the integral diverge?

Answer 1

when the limit doesn’t exist

Question 2

Assuming g(x) is greater than f(x) what do we know about convergence and divergence?

Answer 2

if g(x) converges, then so do f(x)
if f(x) diverges, so does g(x)

Question 3

For a type 1 improper integral (-infinity to infinity), when will the integral converge?

Answer 3

when both integrals (-infinity to 0 and 0 to infinity) exist

Question 4

For a type 1 improper integral (0 to infinity or -infinity to 0), when will the integral converge?

Answer 4

when the limit exists