Question

e^x -x-1/x limit x to 0
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Answer 1

$\large\underline\blue{\bold{Given \:  Question :-  }}$

$\bf \:  ⟼ \bf \:\lim_{x\to\ \: 0}\dfrac{ {e}^{x} - x - 1}{x}$

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$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge \red{AηsωeR} ✍$

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Method :-

Method :- L - H method

$\bf \:  ⟼ \bf \:\lim_{x\to\ \: 0}\dfrac{ {e}^{x} - x - 1}{x}$

$\bf \:  ⟼ \bf \:\lim_{x\to\ \: 0}\dfrac{ \dfrac{d}{dx} ({e}^{x} - x - 1)}{\dfrac{d}{dx} x}$

$\bf \:  ⟼ \bf \:\lim_{x\to\ \: 0} \: ( {e}^{x} - 1)$

$\bf\implies \: \: = 1 - 1 = 0$

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$\large{\boxed{\boxed{\bf{Hence, \bf \:  ⟼ \bf \:\lim_{x\to\ \: 0}\dfrac{ {e}^{x} - x - 1}{x} = 0}}}}$