# How do you find the linearization at a=0 of #f(x)=1/1/(sqrt(2+x))#?

f(x)=1/1/(sqrt(2+x))

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To find the linearization at ( a = 0 ) of ( f(x) = \frac{1}{\sqrt{2+x}} ), we first find the derivative of ( f(x) ) at ( x = 0 ). The derivative ( f'(x) ) can be calculated using the chain rule, and then evaluated at ( x = 0 ). The linearization ( L(x) ) at ( a = 0 ) is given by the equation:

[ L(x) = f(a) + f'(a)(x - a) ]

After substituting ( a = 0 ) and ( f(x) = \frac{1}{\sqrt{2+x}} ), along with the derivative ( f'(x) ) evaluated at ( x = 0 ), we can simplify to obtain the linearization at ( a = 0 ) of the function ( f(x) ).

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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.

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.

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.

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