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# Find the linear approximation of the function $g(x) = \sqrt {1 + x}$ at $a = 0$ and use it to approximate the numbers $\sqrt {0.95}$ and $\sqrt {1.1}.$ Illustrate by graphing $g$ and the tangent line.

## $L(x)=1+\frac{1}{3} x, \quad \sqrt{0.95} \approx 0.9833, \quad \sqrt{1.1} \approx 1.033$

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

Okay, Jim zero is the cube root of one plus zero, which is one therefore, G prime of acts is 1/3 times. Now we're playing in zero. So one plus zero to the negative to over three simplifies to 1/3 plug into the blender or ization formula with sequels one plus 1/3 axe. So now we have one plus X equals 0.95 they're for ox equals negative 0.5 Therefore, we have one plus 1/3 times negative 0.5 0.9833 You know The cube root of 1.11 plus X is 1.1 an ax 0.11 plus 1/3 time's Your 0.1 is one point 1.3 three.

#### Topics

Derivatives

Differentiation

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp