Answer by Syamaprasad Chakrabarti for Find $\lim_{{x \to 0}} \frac{x - \sin...
According to your question, we have to find $$\lim_{x\to0} \frac{x-\sin(x)}{x-\tan(x)}$$. Now the series expansion of $\sin(x)$ is $x-\frac{x^{3}}{3!}+\frac{x^{5}}{5!}-...$ and the series expansion of...
View ArticleAnswer by xpaul for Find $\lim_{{x \to 0}} \frac{x - \sin x}{x - \tan x}$...
Using Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor, one has$$ \begin{eqnarray}&&\lim_{x\to0}\frac{x-\tan...
View ArticleFind $\lim_{{x \to 0}} \frac{x - \sin x}{x - \tan x}$ without using...
I'm trying to find this limit:$$\lim_{{x \to 0}} \frac{x - \sin x}{x - \tan x}$$I want to use only algebraic manipulations and trigonometric identities, without L'Hôpital's rule or Taylor series.I...
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