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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Part D
Transcribed Image Text: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.
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