Which of the following gives the derivative of a function at according to the limit…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Which of the following gives the derivative of a function ff at x=ax=a according to the limit definition? (a) f′(a)=lim⁡h→0f(a)−f(a+h)hf'(a)=\displaystyle\lim_{h\to 0}\frac{f(a)-f(a+h)}{h} (b) f′(a)=lim⁡h→af(a+h)−f(a)hf'(a)=\displaystyle\lim_{h\to a}\frac{f(a+h)-f(a)}{h} (c) f′(a)=lim⁡x→af(x)−f(a)x−af'(a)=\displaystyle\lim_{x\to a}\frac{f(x)-f(a)}{x-a} (d) f′(a)=lim⁡h→0f(a+h)−f(a)af'(a)=\displaystyle\lim_{h\to 0}\frac{f(a+h)-f(a)}{a}

Related theory

Browse the problem library