point) Approximate cos(4.6) using a quadratic approximation: First note that cos(4.6) cos(3/2). Let f(x) = cos(x). Then, f'(x) = -sinx and f"(x) = -cosx Let a = 3/2. Then f' (3/2) = -sin(3pi/2) and f" (3/2) = -cos(3pi/2) Q(x), the quadratic approximation to cos(x) at a = 3/2 is: Q(x) = Use Q(x) to approximate cos(4.6). cos(4.6)~
point) Approximate cos(4.6) using a quadratic approximation: First note that cos(4.6) cos(3/2). Let f(x) = cos(x). Then, f'(x) = -sinx and f"(x) = -cosx Let a = 3/2. Then f' (3/2) = -sin(3pi/2) and f" (3/2) = -cos(3pi/2) Q(x), the quadratic approximation to cos(x) at a = 3/2 is: Q(x) = Use Q(x) to approximate cos(4.6). cos(4.6)~
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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Question
100%

Transcribed Image Text:1 point) Approximate cos(4.6) using a quadratic approximation:
First note that cos(4.6) cos(3/2).
Let f(x) = cos(x). Then,
f'(x) = -sinx
and
f"(x) = -cosx
Let a 3x/2. Then
=
f'(31/2) = -sin(3pi/2)
and
f" (3/2) = -cos(3pi/2)
Q(x), the quadratic approximation to cos(x) at a = 3/2 is:
Q(x) =
Use Q(x) to approximate cos(4.6).
cos(4.6) ≈
B
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