Final Answer
$4.670774$
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Step-by-step Solution
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1
Multiplying fractions $\frac{e\left(e^{\left(x-1\right)}-1\right)}{x} \times \frac{x}{2}$
$\lim_{x\to2}\left(\frac{\frac{e}{2}\left(e^{\left(x-1\right)}-1\right)}{1+\frac{-1}{x}}\right)$
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$\lim_{x\to2}\left(\frac{\frac{e}{2}\left(e^{\left(x-1\right)}-1\right)}{1+\frac{-1}{x}}\right)$
Learn how to solve problems step by step online. Find the limit (x)->(2)lim(((e(e^(x-1)-1))/xx/2)/(1+-1/x)). Multiplying fractions \frac{e\left(e^{\left(x-1\right)}-1\right)}{x} \times \frac{x}{2}. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Combine all terms into a single fraction with x as common denominator. When multiplying exponents with same base we can add the exponents.
Final Answer
$4.670774$