Problem Statement: Let f(x) = V1+x. Back in our first semester of calculus, we used a linear approximation L(x) centered at c = improve upon this idea by using the Taylor polynomials centered at e = 0 (or Maclaurin polynomials) for 0 to find an approximation to v1.2. In our second semester, we f(x) to obtain more accurate approximations for 1.2. (a) Compute T1(x) for f(x) = VT+x centered at e = 0. Then compute L(x) for f(x) centered at e = 0. How do T1(r) and L(x) compare? (b) Use T1(a) to approximate V1.2. How accurate is this approximation? Use the Error Bound to deter- mine the accuracy. (Hint: What should æ be for f(x) = V1.2? What is n in the Error Bound formula in this problem?) (c) Compute T3(r) for f(x) = VT+x centered at e = 0. (d) Use T3(x) to approximate v1.2. How accurate is this approximation? Use the Error Bound to deter- mine the accuracy.

Problem Statement: Let f(x) = V1+x. Back in our first semester of calculus, we used a linear approximation L(x) centered at c = improve upon this idea by using the Taylor polynomials centered at e = 0 (or Maclaurin polynomials) for 0 to find an approximation to v1.2. In our second semester, we f(x) to obtain more accurate approximations for 1.2. (a) Compute T1(x) for f(x) = VT+x centered at e = 0. Then compute L(x) for f(x) centered at e = 0. How do T1(r) and L(x) compare? (b) Use T1(a) to approximate V1.2. How accurate is this approximation? Use the Error Bound to deter- mine the accuracy. (Hint: What should æ be for f(x) = V1.2? What is n in the Error Bound formula in this problem?) (c) Compute T3(r) for f(x) = VT+x centered at e = 0. (d) Use T3(x) to approximate v1.2. How accurate is this approximation? Use the Error Bound to deter- mine the accuracy.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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