Answered: For what values of x does (g(x)=x-sinx)…

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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I need help with this problem with the steps:

For what values of x does (g(x)=x-sinx) have a horizontal tangent line?

I know that (sinx/x=1) but I dont understand what it means by trying to find the values of x. Does it mean I have to plug in like 0.1,0.001,0.0001? Please help. Thank you so much.

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(g(x)=0) because (sin(x)=0) is that why?

It becomes 1 because the (cos(x) = 1) is that why too?

I'm confused by the (2pi), is it always going to be the case where (cos(x)=1) be a multiple of (2pi)? Is (2pi(m)) used to just signify all that it represents all values that can satisfy an horizontal tangent line?

Thank you so much again. The explanation for me was extremely helpful and I understand better.

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