Answer:
a. 4
Step-by-step explanation:
We want to find;
[tex]\lim_{h \to 0} \frac{f(2+h)-f(2)}{h}[/tex]
If [tex]f(x)=x^2[/tex].
[tex]f(2+h)=(2+h)^2[/tex]
[tex]f(2+h)=4+4h+h^2[/tex]
Also;
[tex]f(2)=2^2[/tex]
[tex]f(2)=4[/tex]
This implies that;
[tex]\lim_{h \to 0} \frac{4+4h+h^2-4}{h}[/tex]
Simplify;
[tex]\lim_{h \to 0} \frac{4h+h^2}{h}[/tex]
Factor to get;
[tex]\lim_{h \to 0} \frac{h(4+h)}{h}[/tex]
Cancel the common factors.
[tex]\lim_{h \to 0} 4+h[/tex]
Substitute h=0 to get
[tex]\lim_{h \to 0} 4+h=4+0=4[/tex]
