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8th Edition

Stewart + 1 other

Publisher: Brooks Cole

ISBN: 9781305271845

Chapter 11.11, Problem 3PT

Textbook Problem

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What degree Taylor polynomial about *a* = 1 is needed to approximate *e*^{1.05} accurate to within 0.0001?

- a)
*n*= 2 - b)
*n*= 3 - c)
*n*= 4 - d)
*n*= 5

To determine

For what value of *n*,

**Result used:**

Taylor’s inequality: If *n*th remainder

**Calculation:**

For what value of *n*,

That is, find the degree of the Taylor’s polynomial for

The *n*th term of the Taylor’s polynomial for *a* = 1 is,

Therefore,

By Taylor’s inequality,

Since

Given that

From inequalities (1) and (2),

Study Guide for Stewart's Multivariable Calculus, 8th

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Ch. 11.1 - limnn2+3n2n2+n+1= a) 0 b) 12 c) 1 d)Ch. 11.1 - Sometimes, Always, or Never: If an bn 0 for all...Ch. 11.1 - Sometimes, Always, or Never: If anbncn for all n...Ch. 11.1 - Sometimes, Always, or Never: If {an} is increasing...Ch. 11.1 - True or False: an=(1)nn2 is monotonic.Ch. 11.1 - limnarctann2= a) 4 b) 2 c) d) does not existCh. 11.1 - limn2nn!= a) 2 b) 1 c) 0 d) does not existCh. 11.1 - The fourth term of {an} defined by a1 = 3, and...Ch. 11.2 - The third partial sum of n=1nn2+1 is: a) 310 b) 12...Ch. 11.2 - True or False: n=1an converges mean limkn=1an...

Ch. 11.2 - True or False: n=1an converges if and only if...Ch. 11.2 - True or False: If n=1an converges and n=1bn...Ch. 11.2 - The harmonic series is: a) 1 + 2 + 3 + 4 + b)...Ch. 11.2 - True or False: n=1nn+1 converges.Ch. 11.2 - n=12(14)n converges to: a) 94 b) 2 c) 23 d) the...Ch. 11.2 - True or False: 3+113+19127+ is a geometric series.Ch. 11.3 - For what values of p does the series n=11(n2)p...Ch. 11.3 - True or False: If f(x) is continuous and...Ch. 11.3 - True or False: By the Integral Test, n=21nlnn...Ch. 11.3 - True or False: n=11n2/3 is a convergent series.Ch. 11.3 - True or False: n=1n+2(n2+4n+1)2 is a convergent...Ch. 11.3 - For s=n=11n3, an upper bound estimate for s s6...Ch. 11.4 - Sometimes, Always, or Never: If 0 an bn for all...Ch. 11.4 - True or False: n=1n+1n3 is a convergent series.Ch. 11.4 - True or False: n=1n+n3n2/3+n3/2+1 is a convergent...Ch. 11.4 - True or False: n=1cos2(2n)2n is a convergent...Ch. 11.4 - s=n=11n2n converges by the Comparison Test,...Ch. 11.5 - True or False: n=1(1)n+1lnnn2 is a convergent...Ch. 11.5 - True or False: n=1(1)nn+14 is a convergent series.Ch. 11.5 - For what value of n is the nth partial sum within...Ch. 11.5 - True or False: The Alternating Series Test may be...Ch. 11.6 - True or False: If n=1an converges absolutely, then...Ch. 11.6 - True or False: If limn|anan+1|=3, then n=1an...Ch. 11.6 - True or False: Every series must do one of these:...Ch. 11.6 - Which is true about the series n=12nn!? a)...Ch. 11.6 - Which is true about the series n=1(5)n+1nn? a)...Ch. 11.6 - True or False If the series n=1(1)nn3 converges to...Ch. 11.7 - True or False: n=21(lnn)n converges.Ch. 11.7 - True or False: n=167n+8 converges.Ch. 11.7 - True or False: n=1(1)nnn+3 converges.Ch. 11.7 - True or False: n=1enn! converges.Ch. 11.7 - True or False: n=1(1)nn4 converges conditionally.Ch. 11.7 - True or False: n=1(1)n(1.1)n converges absolutely.Ch. 11.8 - Sometimes, Always, or Never: The interval of...Ch. 11.8 - True or False: If a number p is in the interval of...Ch. 11.8 - For f(x)=n=0(x1)n3n, f(x) = a) 0 b) 2 c) 3 d) f(3)...Ch. 11.8 - The interval of convergence of n=1xnn is: a) [1,...Ch. 11.8 - The radius of convergence of n=0n(x5)n3n is: a) 13...Ch. 11.9 - Given that ex=n=0xnn! for all x, a power series...Ch. 11.9 - For f(x)=n=0x2nn!, f(x) = a) n=1x2n1n! b)...Ch. 11.9 - Using 11x=n=0xn for |x| 1, x1x2dx= a) n=0x2n2n b)...Ch. 11.9 - Using 11x=n=0xn for |x| 1 and differentiation,...Ch. 11.9 - From 11x=n=0xn for |x| 1 and substituting 4x2 for...Ch. 11.10 - Given the Taylor Series ex=n=0xnn!, a Taylor...Ch. 11.10 - Using the power series for cos x, the sum of the...Ch. 11.10 - The nth term in the Taylor series centered at 1...Ch. 11.10 - The Taylor polynomial of degree 3 for f(x) = x(ln...Ch. 11.10 - Use the Taylor polynomial of degree 2 for f(x)=x...Ch. 11.10 - True or False: If Tn(x) is the nth Taylor...Ch. 11.10 - If f(x) = sin 2x, an upper bound for |f(n + 1)(x)|...Ch. 11.10 - If we know that |f(n+1)(x)|Mforall|xa|d, then the...Ch. 11.10 - (123)= a) 516 b) 116 c) 58 d) 58Ch. 11.10 - n=0(23n)xn is the binomial series for: a) (1+x)2/3...Ch. 11.10 - Using a binomial series, the Maclaurin series for...Ch. 11.10 - From the Maclaurin series for ln(1 + x) and sin x,...Ch. 11.11 - The quadratic approximation for f(x)=x6 at a = 1...Ch. 11.11 - If the Maclaurin polynomial of degree 2 for f(x) =...Ch. 11.11 - What degree Taylor polynomial about a = 1 is...

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