4) (a) Find a degree 3 power series for the function sin(x) centered at I fla) = f (a) + f(a) (x-a)+ f"(a) (x-a)´+ f"(a) (x-ə) Isin(g) =를 (풍)" 는 sin (g)-돌 - cos (5):- P,(2)= f(5) + f (5) (x-F) + s 12 3! (os 31 (*-) (- 2. 2! 3! 12 (b) use your approximation from part (a) to estimate sin (1) to the nearest. o60 1. 3)-5(1-5)"- (1-5) Sin (): E . (-5)- 3 (1-3)' - (1-5) a.84147080 2 2 4 12 C) Use Taylors Error Theorem to provide a guavan tee of at least how many digits your approximation is accurate to. M/2-a1" (n+1)! %3D 24 24 A 2.067600475 X 10

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 explain to me why you are using 1xpi/180 in this part b?
7:16
Step2
b)
4) a)
fex) = sinx
-7 f () = sin T, = 3
By the Tayler's series
fox) =
have
(x-a)
z (1)
s'W») = ±
t'cx) = csx
f"cx) = - Sinx 7 f'») = -
f"(x) = - csa =7 f"W») = - →
Sub. these velues iw u) , we get
=7
2
+
put 1 = 1° = I* = 0.0175
.. - 3 = - 1.0297
b)
Step3
c)
7 Siw (1) =
+
= 0. 8C60 - 0. 5149 - 0.4591 + 0.09lo
0.957o -0.1740
=7 siw (1) = -0.0170
Was this solution
?
Transcribed Image Text:7:16 Step2 b) 4) a) fex) = sinx -7 f () = sin T, = 3 By the Tayler's series fox) = have (x-a) z (1) s'W») = ± t'cx) = csx f"cx) = - Sinx 7 f'») = - f"(x) = - csa =7 f"W») = - → Sub. these velues iw u) , we get =7 2 + put 1 = 1° = I* = 0.0175 .. - 3 = - 1.0297 b) Step3 c) 7 Siw (1) = + = 0. 8C60 - 0. 5149 - 0.4591 + 0.09lo 0.957o -0.1740 =7 siw (1) = -0.0170 Was this solution ?
4) (a) Find a degree 3 power series for the function sin(x) centered at It
fla) = f (2) + f(a) (x-a) + f"(a) (x-a)´+ f"(a) (x-a)+.
3
ISsin (s) = 를
(o> (5):
Sin(3)-
+
3!
2!
3!
12
(b) use your approximation from part (a) to esti mate sin (i) to the nearest. o60 1.
Sin (1): E (-5)- B (1-5)' - (1-7)'
84147080
12
c) Use taylors Error Theorem to provide a gueyantee of at least how
digits your approximation is accurate to.
M/2-a"
(n+1)
Many
24
24
A 2.067600475 X 10
Transcribed Image Text:4) (a) Find a degree 3 power series for the function sin(x) centered at It fla) = f (2) + f(a) (x-a) + f"(a) (x-a)´+ f"(a) (x-a)+. 3 ISsin (s) = 를 (o> (5): Sin(3)- + 3! 2! 3! 12 (b) use your approximation from part (a) to esti mate sin (i) to the nearest. o60 1. Sin (1): E (-5)- B (1-5)' - (1-7)' 84147080 12 c) Use taylors Error Theorem to provide a gueyantee of at least how digits your approximation is accurate to. M/2-a" (n+1) Many 24 24 A 2.067600475 X 10
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