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Recall that the volume of a sphere of radius r is V(r) = \frac{4\pi r^{3}}{3}. Find L, the...

Question:

Recall that the volume of a sphere of radius r is {eq}V(r) = \frac{4\pi r^{3}}{3} {/eq}.

Find L, the linearisation of V(r) at r = 30.

L(r) = A

sphere of radius 30 centimeters is covered with a layer of paint of thickness 0.45 millimeters. Use the linearisation of V at r = 30 to estimate the volume of paint that is used. cubic centimeters of paint, help (numbers)

Linearization of a function

One of the applications of differentiation is Linearization.

Any function can be approximated as a linear function using derivative. Usually linearization is calculated at a given value of x.

If {eq}f(x) {/eq} is the given function, then it's linearization at {eq}x = a {/eq} is given by,

{eq}L(x) = f(a) + f'(a)(x-a) {/eq}

Answer and Explanation:

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Volume of a sphere with radius r is given by,

{eq}\displaystyle V(r) = \frac{4 \pi r^3}{3} \\ \therefore V'(r) = 4 \pi r^2 {/eq}

Linearization of...

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Linearization of Functions

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Chapter 10 / Lesson 1
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Over the river and through the woods to Grandmother's house we go ... Are we there yet? In this lesson, apply linearization to estimate when we will finally get to Grandma's house!


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