3. (4 pts) Determine whether or not the following improper integrals converge, either by integrating directly orcomparing them with a known integral:(a)Z∞1lnxxdx.
4. (The power of exponential growth) Alice promises to pay Bob $1000 today, $2000 in one year, $3000 in two years,and so on indefinitely. Assume that the interest rate is 2%, compounded continuously.(a) (4 pts) Express the total present value of Alice’s promise to Bob as an indefinite integral, and evaluate it.