Find the limit $\lim_{x\to0}\left(\frac{\frac{\frac{e}{2}\left(e^x-1\right)}{e}\left(x+1\right)}{x+1}\right)$

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$\lim_{x\to0}\left(\frac{\frac{\frac{e}{2}\left(e^x-1\right)}{e}\left(x+1\right)}{x+1}\right)$

Learn how to solve problems step by step online. Find the limit (x)->(0)lim(((e/2(e^x-1))/e(x+1))/(x+1)). Simplifying. Simplify the fraction \frac{\frac{\frac{e}{2}\left(e^x-1\right)}{e}\left(x+1\right)}{x+1} by x+1. Take \frac{\frac{e}{2}}{e} out of the fraction. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}.