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

Linearization is finding the linear approximation to a function at a given point

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To find the linearization of ( f(x) = \frac{1}{\sqrt{2+x}} ) at the point ( a = 0 ), follow these steps:

- Find the first derivative ( f'(x) ) of the function.
- Evaluate ( f'(0) ) to find the slope of the tangent line at ( x = 0 ).
- Use the point-slope form of the equation for a line, ( y - y_1 = m(x - x_1) ), where ( m ) is the slope and ( (x_1, y_1) ) is the point of tangency (in this case, ( x_1 = 0 ) and ( y_1 = f(0) )).
- Simplify the equation obtained in step 3 to get the linearization of ( f(x) ) at ( a = 0 ).

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