Problem 11. For this problem you may use the fact that the Taylor series of cos(I) centered at zero is cos(x) = (-1)*,2k (2k)! =1- 2! 10 +... 10! 4! 6! 8! k=0 1. Use the Taylor series of cos(x) to find the first 5 nonzero terms in the Taylor series of 2(cos(x)- 1) f(1) = centered at zero. Hint: Start by subtracting 1 from the Taylor series. 2. Use your answer to the previous part to compute the limit: 2(cos(x) – 1) lim
Problem 11. For this problem you may use the fact that the Taylor series of cos(I) centered at zero is cos(x) = (-1)*,2k (2k)! =1- 2! 10 +... 10! 4! 6! 8! k=0 1. Use the Taylor series of cos(x) to find the first 5 nonzero terms in the Taylor series of 2(cos(x)- 1) f(1) = centered at zero. Hint: Start by subtracting 1 from the Taylor series. 2. Use your answer to the previous part to compute the limit: 2(cos(x) – 1) lim
Hi there please help me with this problem and explain it. It goes together but if you cannot make both please just solve #11 thanks
Transcribed Image Text:Problem 10. The power series from the previous problem is the Taylor series for f(a) = e .
00
(-1)*2k
x2
= 1-
1!
a4
p(x) =E
k!
2!
k=0
Verify that this is correct by computing the degree 4 Taylor polynomial of f(r) = e- centered at
zero.
Problem 11. For this problem you may use the fact that the Taylor series of cos(x) centered at
zero is
(-1)*72k
(2k)!
g10
+..
10!
cos(r)
=1-
2!
6!
8!
4!
k=0
1. Use the Taylor series of cos(x) to find the first 5 nonzero terms in the Taylor series of
2(cos(z) – 1)
f(2) =
centered at zero.
Hint: Start by subtracting 1 from the Taylor series.
2. Use your answer to the previous part to compute the limit:
2(cos(x) – 1)
lim
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