** Final answer to the problem

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** Step-by-step Solution **

** How should I solve this problem?

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- Solve using L'H么pital's rule
- Solve without using l'H么pital
- Solve using limit properties
- Solve using direct substitution
- Solve the limit using factorization
- Solve the limit using rationalization
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
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If we directly evaluate the limit $\lim_{x\to 0}\left(\frac{e^{2x}-e^{-2x}-4x}{x-\sin\left(x\right)}\right)$ as $x$ tends to $0$, we can see that it gives us an indeterminate form

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

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Learn how to solve limits by direct substitution problems step by step online. Find the limit of (e^(2x)-e^(-2x)-4x)/(x-sin(x)) as x approaches 0. If we directly evaluate the limit \lim_{x\to 0}\left(\frac{e^{2x}-e^{-2x}-4x}{x-\sin\left(x\right)}\right) as x tends to 0, we can see that it gives us an indeterminate form. We can solve this limit by applying L'H么pital's rule, which consists of calculating the derivative of both the numerator and the denominator separately. After deriving both the numerator and denominator, the limit results in. If we directly evaluate the limit \lim_{x\to 0}\left(\frac{2e^{2x}+2e^{-2x}-4}{1-\cos\left(x\right)}\right) as x tends to 0, we can see that it gives us an indeterminate form.

** Final answer to the problem

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