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Find the limit $\lim_{x\to0}\left(\frac{x-\sin\left(x\right)}{x\tan\left(x\right)}\right)$

Step-by-step Solution

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Final Answer

The limit does not exist

Step-by-step Solution

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Split the fraction $\frac{x-\sin\left(x\right)}{x\tan\left(x\right)}$ in two fractions with common denominator $x\tan\left(x\right)$

$\lim_{x\to0}\left(\frac{x}{x\tan\left(x\right)}+\frac{-\sin\left(x\right)}{x\tan\left(x\right)}\right)$

Learn how to solve limits by direct substitution problems step by step online.

$\lim_{x\to0}\left(\frac{x}{x\tan\left(x\right)}+\frac{-\sin\left(x\right)}{x\tan\left(x\right)}\right)$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(0)lim((x-sin(x))/(xtan(x))). Split the fraction \frac{x-\sin\left(x\right)}{x\tan\left(x\right)} in two fractions with common denominator x\tan\left(x\right). Simplify the fraction \frac{x}{x\tan\left(x\right)} by x. Simplify \frac{-\sin\left(x\right)}{x\tan\left(x\right)} by applying trigonometric identities. The limit of a sum of two or more functions is equal to the sum of the limits of each function: \displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x)).

Final Answer

The limit does not exist

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Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by FactoringLimits by Rationalizing

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Function Plot

Plotting: $\mathrm{The\:limit\:does\:not\:exist}$

Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

Used Formulas

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