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Olá Gabriel!
![\\ \mathsf{\lim_{h \to 0} \frac{(x + h)^2 - x^2}{h} =} \\\\\\ \mathsf{\lim_{h \to 0} \frac{[(x + h) + x][(x + h) - x]}{h} =} \\\\\\ \mathsf{\lim_{h \to 0} \frac{(2x + h) \cdot h}{h} =} \\\\\\ \mathsf{\lim_{h \to 0} (2x + h) =} \\\\\\ \mathsf{2x + 0 =} \\\\\\ \boxed{\mathsf{2x}}](https://tex.z-dn.net/?f=%5C%5C+%5Cmathsf%7B%5Clim_%7Bh+%5Cto+0%7D+%5Cfrac%7B%28x+%2B+h%29%5E2+-+x%5E2%7D%7Bh%7D+%3D%7D+%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B%5Clim_%7Bh+%5Cto+0%7D+%5Cfrac%7B%5B%28x+%2B+h%29+%2B+x%5D%5B%28x+%2B+h%29+-+x%5D%7D%7Bh%7D+%3D%7D+%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B%5Clim_%7Bh+%5Cto+0%7D+%5Cfrac%7B%282x+%2B+h%29+%5Ccdot+h%7D%7Bh%7D+%3D%7D+%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B%5Clim_%7Bh+%5Cto+0%7D+%282x+%2B+h%29+%3D%7D+%5C%5C%5C%5C%5C%5C+%5Cmathsf%7B2x+%2B+0+%3D%7D+%5C%5C%5C%5C%5C%5C+%5Cboxed%7B%5Cmathsf%7B2x%7D%7D "\\ \mathsf{\lim_{h \to 0} \frac{(x + h)^2 - x^2}{h} =} \\\\\\ \mathsf{\lim_{h \to 0} \frac{[(x + h) + x][(x + h) - x]}{h} =} \\\\\\ \mathsf{\lim_{h \to 0} \frac{(2x + h) \cdot h}{h} =} \\\\\\ \mathsf{\lim_{h \to 0} (2x + h) =} \\\\\\ \mathsf{2x + 0 =} \\\\\\ \boxed{\mathsf{2x}}")
Gabriel12mm:
vlw mano...
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