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Question Number 170159 by mathlove last updated on 17/May/22

lim_(x→4)  ((e !x−24)/( (√x)−2))=?

$$\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\:\frac{{e}\:!{x}−\mathrm{24}}{\:\sqrt{{x}}−\mathrm{2}}=? \\ $$

Answered by Mathspace last updated on 18/May/22

hosital  lim=lim_(x→4)    ((e!)/(1/(2(√x))))  =lim_(x→4)  2(e)!(√x)  =4(e)!

$${hosital}\:\:{lim}={lim}_{{x}\rightarrow\mathrm{4}} \:\:\:\frac{{e}!}{\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}} \\ $$$$={lim}_{{x}\rightarrow\mathrm{4}} \:\mathrm{2}\left({e}\right)!\sqrt{{x}} \\ $$$$=\mathrm{4}\left({e}\right)! \\ $$

Commented by mathlove last updated on 18/May/22

no e!    it ′s   !x

$${no}\:{e}!\:\:\:\:{it}\:'{s}\:\:\:!{x} \\ $$

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