b)
\(\mathbf{f(x) = \frac{x^2 - 4}{x + 2}}\)
\(\mathbf{\Rightarrow f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}}\)
\(\mathbf{\Rightarrow f'(x) = \lim_{h \to 0} \frac{\frac{(x + h)^2 - 4}{(x + h) + 2} - \frac{x^2 - 4}{x + 2}}{h}}\)
\(\mathbf{\Rightarrow f'(x) = \lim_{h \to 0} \frac{\frac{[(x + h) + 2][(x + h) - 2]}{(x + h) + 2} - \frac{(x + 2)(x - 2)}{x + 2}}{h}}\)
\(\mathbf{\Rightarrow f'(x) = \lim_{h \to 0} \frac{\frac{(x + h + 2)(x + h - 2)}{x + h + 2} - \frac{(x + 2)(x - 2)}{x + 2}}{h}}\)
\(\mathbf{\Rightarrow f'(x) = \lim_{h \to 0} \frac{(x + h - 2) - (x - 2)}{h}}\)
\(\mathbf{\Rightarrow f'(x) = \lim_{h \to 0} \frac{x + h - 2 - x + 2}{h}}\)
\(\mathbf{\Rightarrow f'(x) = \lim_{h \to 0} \frac{h}{h}}\)
\(\boxed{\mathbf{\Rightarrow f'(x) = 1}}\)
Editado pela última vez por
danjr5 em 18 Oct 2020, 13:27, num total de 1 vez.
Razão: Corrigir LaTeX