Which of the following limits equals the instantaneous rate of change of a…

MATHEMATICS · Single correct · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

Which of the following limits equals the instantaneous rate of change of a differentiable function

f

x=a

? (a)

\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{a+h}

(b)

\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a-h)}{h}

(c)

\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{h}

(d)

\displaystyle \lim_{x\to a}\frac{f(a)-f(x)}{x-a}