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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View this answerGiven 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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