This is my sixth question on my PSET

6. (a) Find f: % dt, where at > 0. (b) One way to dene the natural log, hlzr, is as the denite integral f: % tit. Sketch the graph of l/t and approximate ln2 numerically by partitioning the interval [1,2] into 4 equal pieces and computing L4 and R4. Write out each sum long-hand, without using a calculator program. (c) Which one of the approximating sums, L4 or R4, do you expect is a better approximation of 1112? Explain. (d) Use the Error Bounding formula for L1n and Rn to nd an upper bound on the error in the approx imations you found in part (a). Once you have found your error bound, state its relationship to your approximation (e.g. \"My approximation of ln2 is at most (your error bound) away from the exact value.\") (e) Suppose we used n, : 100 slices instead of 4. What is an upper bound on the error in our approximations? Once you've found the error bound, explicitly state its relationship to the L100 or R100 approximation in a sentence, as in the previous part. (You don't need to compute L100 or R100 to write this sentence!) (f) Into how many equal pieces would we need to split the interval [1, 2] in order to approximate 1112 so that the error in our lefthand and righthand approximations is guaranteed to be less than 1/10000? (You don't need to nd the very best number of pieces, just one that you can be sure that works!)