Question

Lim(3+h)2 - 9/h quando h tende a 0?

Answer 1

$\underset{h\to 0}{\mathrm{\ell im}}~\dfrac{(3+h)^2-9}{h}\\\\\\=\underset{h\to 0}{\mathrm{\ell im}}~\dfrac{\diagup\!\!\!\! 9+6h+h^2-\diagup\!\!\!\! 9}{h}\\\\\\ =\underset{h\to 0}{\mathrm{\ell im}}~\dfrac{6h+h^2}{h}\\\\\\ =\underset{h\to 0}{\mathrm{\ell im}}~\dfrac{\diagup\!\!\!\! h\cdot (6+h)}{\diagup\!\!\!\! h}\\\\\\ =\underset{h\to 0}{\mathrm{\ell im}}~(6+h)$


$=6+0\\\\\\ =6$


Bons estudos! :-)