I need help in this problem . Any mention of the logarithm function within this

Question

I need help in this problem .

Any mention of the logarithm function within this problem will invalidate the part of the answer where it appears. Let G(x) be the function defined by G(x):= Area under the curve f(t) = 1/t, between t = 1 and t = x (see figure 3). Figure 3: Area under the function 1/t. Recall that an area computed from right to left has the opposite sign of the one computed from left to right. Express G(x) as a definite integral. What is the value of G at x = 1. In other words, what is G(1)? Use the expression you found in (i) and a comparison of areas to show that h/h + x 0. Using the limit definition of the derivative of G, namely show that G(x) is an antiderivative of x-1. That is, show that G"(x) = 1/x. To simplify the computation you may assume that h > 0 in (5). Apply the sandwich theorem to (4) in part (iii).

Explanation / Answer

let the area divided in to n parts , each of length h so ,G(x) = integral of G(x+h)-G(x) limit of integration would be from 0 to nh 2) G(1) is 1

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