Question

.Encontrar la derivada mediante límites de

Porfa ayúdenme :(
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Answer 1

Respuesta:

1.

$f'(x) = 3$

2.

$f'(x) = 2x-1$

Explicación paso a paso:

1.

$\lim_{h \to 0}\frac {((3(x+h)-7)-(3x-7)}{h}\\\lim_{h\to0}\frac{3x+3h-7-3x+7}{h} \\\lim_{h \to 0}\frac{3h}{h} = 3$

2.

$\lim_{h \to 0}\frac {({(x+h)}^{2}-(x+h)+1)-({x}^{2}-x+1)}{h} \\\lim_{h\to0}\frac{{x}^{2}+2xh+{h}^{2} -x - h +1 - {x}^{2} +x-1}{h} \\ \lim_{h \to 0}\frac{2xh+{h}^{2}-h}{h} \\ \lim_{h \to 0} \frac {2xh}{h}+\frac{{h}^{2}}{h}-\frac{h}{h}\\ \lim_{h \to 0} 2x+h-1\\ =2x-1$