Question

If f(x)=x^2 find lim h -> 0 {f(x+h)-f(x)}/h

Answer 1

Question #74270, Math / Other

If $f(x) = x^2$ find $\lim_{h \to 0} \frac{(f(x+h)) - f(x)}{h}$.

Answer.

$$\lim_{h \to 0} \frac{f(x+h) - f(x)}{h} = \lim_{h \to 0} \frac{(x+h)^2 - x^2}{h} = \lim_{h \to 0} \frac{2xh + h^2}{h} = 2x$$

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