25-07-2022
Mathematics

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lim f(x) 2^x-1/x. Find the limit of x as x approaches 0

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LammettHash LammettHash

25-07-2022

The limit happens to be the derivative of [tex]2^x[/tex] at [tex]x=0[/tex]:

[tex]\displaystyle f'(c) = \lim_{x\to c}\frac{f(x)-f(c)}{x-c} \implies \lim_{x\to0} \frac{2^x - 1}x = (2^x)'\bigg|_{x=0} = \ln(2)\,2^x \bigg|_{x=0} = \boxed{\ln(2)}[/tex]

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