ANSWER
[tex]a. \: 4[/tex]
EXPLANATION
Given:
[tex]f(x) = {x}^{2} [/tex]
[tex]f(2) = 4[/tex]
[tex]f(2 + h) = {(2 + h)}^{2} [/tex]
[tex]f(2 + h) = {h}^{2} + 4h + 4[/tex]
[tex]lim_{h\to 0} \frac{f(x + h) - f(2)}{h} [/tex]
Substitute;
[tex]lim_{h\to 0} \frac{ {h}^{2} + 4h + 4 - 4}{h} [/tex]
[tex]lim_{h\to 0} \frac{ {h}^{2} + 4h }{h} [/tex]
[tex]lim_{h\to 0} h + 4[/tex]
Plug in zero,
[tex] = 0 + 4[/tex]
[tex] = 4[/tex]
