Question

f:R->R, f(x)= 3e² + x²

Aratati ca $\lim_{x \to 0} \frac{f(x) - f(0)}{x} = 3$

Dau fundă pentru cine rezolvă exercițiul

Answer 1

$\it f:\mathbb{R}\rightarrow \mathbb{R},\quad f(x) = 3e^2+x^2\\ \\ \lim\limits_{x\to 0}\dfrac{f(x)-f(0)}{x} =\lim\limits_{x\to 0}\dfrac{f(x)-f(0)}{x-0} = f'(0)=\boxed{0}\\ \\ f'(x) = 2x$