Which of the following limits equals the derivative of at ?

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

Problem

Which of the following limits equals the derivative of

f(x)=x^{2}

x=3

? (a)

\displaystyle \lim_{h\to0}\frac{(3+2h)^{2}-9}{h}

(b)

\displaystyle \lim_{h\to0}\frac{(3+h)^{2}-9}{h}

(c)

\displaystyle \lim_{h\to0}\frac{(3+h)^{2}-9}{2h}

(d)

\displaystyle \lim_{h\to0}\frac{(3+h)^{3}-27}{h}