2930 The limit of an indeterminate form as xx0 can sometimesbe found by expanding the

Chapter 9, Problem 29

(choose chapter or problem)

The limit of an indeterminate form as $x \rightarrow x 0$ can sometimes

be found by expanding the functions involved in Taylor

series about $x=x 0$ and taking the limit of the series term by

term. Use this method to find the limits in these exercises.

$\text { (a) } \lim _{x \rightarrow 0} \frac{\sin x}{x}$

$\text { (b) } \lim _{x \rightarrow 0} \frac{\tan ^{-1} x-x}{x^{3}}$

Equation Transcription:

$x\rightarrow{}x0$

$x=x0$

$\lim\limits_{{x} \rightarrow {0}}\frac{sinx}{x}$

$\lim\limits_{{x} \rightarrow {0}}\frac{ta{n}^{-1}x-x}{{x}^{3}}$

Text Transcription:

X right arrow x0

x=x0

Lim x right arrow 0 sinx/x

Lim x right arrow 0 tan^-1 x-x/x^3

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