. The exponential function, exp : R - R, is the unique function f that satisfies f'(x) = f(x) for all x E R and f (0) = 1. The natural logarithm, log, is the function inverse to the exponential function, exp: that is, for all x E R and for all y > 0, y = exp (x) if and only if x = log (y). a. Compute the definite integral ($ 20-1 dx. b. Using your result from part a. and any appropriate rules for computing limits, show that rexp t lim x-dx = t. You may use [exp (t)]" = exp (at) for all real a without proof. c. Explain how, from your answers to parts a. and b., we may justify x dx = log s