Math  /  Calculus

Questiony=(4+x)1/2,a=0y=(4+x)^{-1 / 2}, \quad a=0
Find the Linearization at x=ax=a. L(x)=L(x)=

Studdy Solution
Use the linearization formula L(x)=y(a)+dydxx=a(xa) L(x) = y(a) + \frac{dy}{dx} \bigg|_{x=a} (x - a) :
L(x)=12+(116)(x0) L(x) = \frac{1}{2} + \left(-\frac{1}{16}\right)(x - 0)
L(x)=12116x L(x) = \frac{1}{2} - \frac{1}{16}x
The linearization of the function at x=0 x = 0 is:
L(x)=12116x L(x) = \frac{1}{2} - \frac{1}{16}x

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