Question

lim. x give 0 (e^x-1)÷x please anyone with humble heart find this answer step by step​

Answer 1

Given :

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

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To Find :

• The value of lim x tends to 0=?

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Solution :

$\\ \implies\sf{lim_{x \to 0 } \: \: \dfrac{e^{x} -1}{x}}$

By applying L-hospital rule:

$\\ \implies\sf{lim_{x \to 0} \: \: \dfrac{dy}{dx} \dfrac{e^{x} -1}{x}}$

$\\ \implies\sf{lim_{ x \to 0} \: \: \dfrac{e^{x} -0}{1}}$

$\\ \implies\sf{lim_{x \to 0} \: \: {e^{x}}}$

As we know that e^0 =1

$\\ \implies\sf{lim_{x \to 0 } \: \: e^{0}}$

$\\ \implies \sf{lim_{ x \to 0} \: \: 1}$

$\\ \therefore\red\bigstar{\boxed{\sf{lim_{ x \to 0} \: \: \: 1}}}$