1.9 1.99 2.01 2.1 f(x) T(x) 2.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Topic Video
Question

Find the tangent line approximation T to the graph of f at the given point. Then complete the table.    f(x) = sin x,      (2, sin 2)

1.9
1.99
2.01
2.1
f(x)
T(x)
2.
Transcribed Image Text:1.9 1.99 2.01 2.1 f(x) T(x) 2.
Expert Solution
Step 1

The given function fx=sin x.

We have to find the tangent line approximation at the point x=2.

Step 2

The tangent line approximation of fx at x=c is Tx=fc+f'cx-c

fx=sin x

f2=sin 2

Differentiate with respect to x,

f'c=cos x

f'2=cos 2

Now, the tangent line approximation of fx at x=2,

Tx=f2+f'2x-cTx=sin 2+cos 2x-2

The tangent line approximation is  Tx=sin 2+cos 2x-2.

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