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Grade 12Differential Calculus

how to check diffrentiability of e^-xat x=0

Shivam

12 Years agoGrade 12

1 Answer

Arun Kumar

12 Years ago

Hi

we will find this

$\\lim_{x \to 0} {f(c+h)-f(c) \over h} \\=>\\lim_{x \to 0+}={f(0+h)-f(0) \over h}={e^{-h}-e^{0} \over h} \\$form is 0/0 so L hospital $ \\=>\\lim_{x \to 0+}=e^{-0}=1 \\\\lim_{x \to 0-}={f(0-h)-f(0) \over -h}={e^{+h}-e^{0} \over -h} \\$form is 0/0 so L hospital $ \\=>\\lim_{x \to 0-}=e^{-0}=1$

both exist and equal to same no. so we say it is differentiable around 0

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

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