Determine whether the following statements are true or false. Circle your respon

Question

Determine whether the following statements are true or false. Circle your response and give a brief explanation (a reason why it's true or an example where it fails). TRUE FALSE Suppose that f is a continuous function on (-infinity, infinity). Then integral_-infinity^+infinity f(x) dx = lim_R right arrow +infinity integral_-R^R f(x) dx. TRUE FALSE Let g be a continuous function on [0, +infinity) such that lim_x right arrow +infinity g(x) = 1. Then the improper integral integral_0^+infinity g(x) dx is always divergent.

Explanation / Answer

a) True

B) False

Because (1-e^-x) value tends to 1 as x tends to infinity but it is convergent in 0 to infinity limits

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