Question

lim [2xh + h² + h]/h = f'(x)
h → 0
lim [h(2x + h + 1)]/h = f'(x)
h → 0 PQ DO (=1) ALI???

Answer 1

Colocaram h em evidência, e $\frac{h}{h}=1~se~h\neq0$

$\lim\limits_{h\to0}\dfrac{2xh+h^{2}+h}{h}$

Colocando h em evidência no numerador:

$\lim\limits_{h\to0}\dfrac{h\cdot(2x+h+1)}{h}\\\\\\=\lim\limits_{h\to0}(2x+h+1)\\\\\\=2x+0+1\\\\=2x+1$
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Note que $h\cdot(2x+h+1)=2x\cdot h+h\cdot h+1\cdot h=2xh+h^{2}+h$