3. (a) Find the 5th order Taylor polynomial about a = 7 for sin x. (b) Use this Taylor polynomial to approximate sin in terms of powers of 2. 11T (c) The remainder term for a polynomial of order n expanded about x = a is R„(x) = f(n+1)(c). (x – a)n+1 (n + 1)! where c lies between a and x. Write down the remainder term for the polynomial that you have found in part (a). (d) Use the remainder term that you have found in part (c) to show that theTaylor polynomial approximation to sin that you found in part (b) is within 10-6 of the actual value of sin . Use your calculator to verify that the difference between sin and your approximation is, indeed, less than 10-6. 12 : 11T
3. (a) Find the 5th order Taylor polynomial about a = 7 for sin x. (b) Use this Taylor polynomial to approximate sin in terms of powers of 2. 11T (c) The remainder term for a polynomial of order n expanded about x = a is R„(x) = f(n+1)(c). (x – a)n+1 (n + 1)! where c lies between a and x. Write down the remainder term for the polynomial that you have found in part (a). (d) Use the remainder term that you have found in part (c) to show that theTaylor polynomial approximation to sin that you found in part (b) is within 10-6 of the actual value of sin . Use your calculator to verify that the difference between sin and your approximation is, indeed, less than 10-6. 12 : 11T
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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Can you please help me on this exercise for the Taylor's series topic, question 3 part b,c and d, please?
Transcribed Image Text:3.
(a) Find the 5th order Taylor polynomial about a = 1 for sin x.
(b) Use this Taylor polynomial to approximate sin in terms of powers of .
11T
12
(c) The remainder term for a polynomial of order n expanded about x = a is
R„(x) = f(n+1)(c)-
(x – a)n+1
(n+ 1)!
where c lies between a and x. Write down the remainder term for the polynomial
that you have found in part (a).
(d) Use the remainder term that you have found in part (c) to show that theTaylor
polynomial approximation to sin that you found in part (b) is within 10-6 of
the actual value of sin . Use your calculator to verify that the difference between
your approximation is, indeed, less than 10-6.
11т
12
11T
and
sin
12
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