Evaluate the following: \[ \displaystyle \lim_{x\ \to \ 0} \ \dfrac{e^x sinx-x-x^2}{x^2+xlog(1-x)}\]

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Evaluate the following:

$\displaystyle \lim_{x\ \to \ 0} \ \dfrac{e^x sinx-x-x^2}{x^2+xlog(1-x)}$

written 3.9 years ago by

teamques10 ★ 69k

modified 3.4 years ago by

binitamayekar ★ 6.7k

engineering mathematics

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written 3.9 years ago by

teamques10 ★ 69k

$=\lim\limits_{x\rightarrow0}=\dfrac{e^xsinx-x-x^2}{x^2+xlog(1-x)}=-\dfrac{2}{3}$

$=-\dfrac{2}{3}$

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