Final Answer
Step-by-step Solution
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Apply the property of the product of two powers of the same base in reverse: $a^{m+n}=a^m\cdot a^n$
Learn how to solve limits by direct substitution problems step by step online.
$\lim_{x\to0}\left(\frac{\sin\left(x\right)}{e^1e^x-e}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(0)lim(sin(x)/(e^(x+1)-e)). Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Any expression to the power of 1 is equal to that same expression. If we directly evaluate the limit \lim_{x\to 0}\left(\frac{\sin\left(x\right)}{ee^x-e}\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.