Question

The linear approximation for f(x)=cosx at x=pi /2 is L(x)=1-frac{1}{2}(x-frac{pi}{2}). To approximate cos(88∘), we use L(88∘)=1-frac{1}{2}(88-90)=1-frac{1}{2}(-2)=1+1=2. Therefore, cos(88∘) is approximately 2.

Name: the linear approximation for fxcosx at xpi 2 is lx1 frac12x fracpi2 to approximate cos88 we use l881 frac1288 901 frac12 2112 therefore cos88 is approximately 2 41636
Uploaded: 2023-07-20T04:12:08-08:00
Duration: 1 min 48 s
Channel: Madhur L
Description: the linear approximation for fxcosx at xpi 2 is lx1 frac12x fracpi2 to approximate cos88 we use l881 frac1288 901 frac12 2112 therefore cos88 is approximately 2 41636

          The linear approximation for f(x)=cosx at x=pi /2 is L(x)=1-frac{1}{2}(x-frac{pi}{2}). To approximate cos(88∘), we use L(88∘)=1-frac{1}{2}(88-90)=1-frac{1}{2}(-2)=1+1=2. Therefore, cos(88∘) is approximately 2.

Added by Soledad L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/20/2023

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Step 1: The linear approximation for f(x)=cosx at x=\pi /2 is given by L(x)=1-\frac{1}{2}(x-\frac{\pi}{2}). Show more…

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The linear approximation for f(x)=cosx at x=pi /2 is L(x)=1-frac{1}{2}(x-frac{pi}{2}). To approximate cos(88∘), we use L(88∘)=1-frac{1}{2}(88-90)=1-frac{1}{2}(-2)=1+1=2. Therefore, cos(88∘) is approximately 2.