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Question Number 175995 by sciencestudent last updated on 10/Sep/22

lim_(x→0) ((e^(3x) −1)/x)=?

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{e}^{\mathrm{3}{x}} −\mathrm{1}}{{x}}=? \\ $$

Answered by Ar Brandon last updated on 10/Sep/22

lim_(x→0) ((e^(3x) −1)/x)=lim_(x→0) (((1+3x)−1)/x)=3

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{3}{x}} −\mathrm{1}}{{x}}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+\mathrm{3}{x}\right)−\mathrm{1}}{{x}}=\mathrm{3} \\ $$

Answered by riyaziyyatelmlerinsahi last updated on 10/Sep/22

Answer:Ibrahim Abdullayev  lim_(x→0) ((e^(3x) -1)/x)=lim_(x→0) (((e^(3x) -1)′)/(x′))=lim_(x→0) ((3e^(3x) )/1)=3∙lim_(x→0) e^(3x) =3∙1=3.

$${Answer}:{Ibrahim}\:{Abdullayev} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{3}{x}} -\mathrm{1}}{{x}}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({e}^{\mathrm{3}{x}} -\mathrm{1}\right)'}{{x}'}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{3}{e}^{\mathrm{3}{x}} }{\mathrm{1}}=\mathrm{3}\centerdot\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{e}^{\mathrm{3}{x}} =\mathrm{3}\centerdot\mathrm{1}=\mathrm{3}. \\ $$

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