# Using linearization, determine the approximation of {eq}f(x,y) = x^2 + y^2 {/eq} at {eq}(1.05, 1.05) {/eq}.

## Question:

Using linearization, determine the approximation of {eq}f(x,y) = x^2 + y^2 {/eq} at {eq}(1.05, 1.05) {/eq}.

## Partial Derivatives:

Let's say we have a multivariable function {eq}\displaystyle f(x,y) {/eq}. Using linearization of the function over the interval {eq}\displaystyle (x,y) \to (x+dx,y+dy) {/eq} we can estimate the value of the function as,

{eq}\displaystyle f(x+dx,y+dy) = f(x,y) + \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y } dy {/eq}

Note that the above expression is valid only if {eq}\displaystyle dx,dy {/eq} are infinitesimally small, but it can be used to approximate the value of the function over small regions.

## Answer and Explanation: 1

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Given a multivariable function,

{eq}\displaystyle f(x,y) = x^2 + y^2 {/eq}

Using linearization we need to determine the approximate value of...

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