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How do you find the linearization of #f(x) = cos(x)# at x=3pi/2?

Answer 1

Evelyn Agard

I got #y=x-4.71#

Have a look:

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Answer 2

Adam Adkins

To find the linearization of ( f(x) = \cos(x) ) at ( x = \frac{3\pi}{2} ), follow these steps:

Calculate the value of ( f(x) ) and its derivative ( f'(x) ) at ( x = \frac{3\pi}{2} ).
Use the formula for the linearization, which is given by ( L(x) = f(a) + f'(a)(x - a) ), where ( a ) is the point of tangency.
Substitute the values of ( f(\frac{3\pi}{2}) ), ( f'(\frac{3\pi}{2}) ), and ( a = \frac{3\pi}{2} ) into the formula to find the linearization function ( L(x) ).

Applying these steps:

( f(\frac{3\pi}{2}) = \cos(\frac{3\pi}{2}) = 0 ) and ( f'(\frac{3\pi}{2}) = -\sin(\frac{3\pi}{2}) = -1 ).
Use the formula for linearization: ( L(x) = f(\frac{3\pi}{2}) + f'(\frac{3\pi}{2})(x - \frac{3\pi}{2}) ).
Substitute the values: ( L(x) = 0 + (-1)(x - \frac{3\pi}{2}) = -x + \frac{3\pi}{2} ).

Therefore, the linearization of ( f(x) = \cos(x) ) at ( x = \frac{3\pi}{2} ) is ( L(x) = -x + \frac{3\pi}{2} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.