Derivatives from limits The following limits represent ƒ′(a)for some function f and some real number a.a. Find a possible function f and number a.b. Evaluate the limit by computing f'(a)limx→0ex−1x

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Derivatives from limits The following limits represent ƒ′(a)for some function f and some real number a.a. Find a possible function f and number a.b. Evaluate the limit by computing f&#039;(a)limx→0ex−1x

lamanocornudaW · Accepted Answer

Given,limx→0ex−1xa). limx→0ex−1x=limx→0ex−e0x−0Now comparing with limx→af(x)−f(a)x−a, we getf(x)=ex and a=0b). The derivative of a function f at x=a is,f′(a)=limx→af(x)−f(a)x−aNow differentiating f(x)=ex with respect to x, we getf′(x)=exNow at x=0f′(0)=e0=1Therefore,limx→0ex−1x=limx→0ex−e0x−0=f′(0) [By the definition of derivative]=1

Derivatives from limits The following limits represent ƒ′(a) for some functi

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