Problem 2. This question is about improper integrals. (1) Assume f(x) > 0 and ƒ is decreasing. Show (using comparison) that if lim×→∞ f(x) L and L > 0, then fo f(x)dx diverges. = (2) If lim→∞ f(x) = 0, must ſo f(x)dx converge? Give a proof if yes, give a counterex- ample if no. (3) Give an example of a function so that 50% f(x)dx diverges even though limb∞ √ f(x)dx: 0. =

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