$[20$ marks$]$

$3.$ Find the limit:

$(4$ marks$)$

a$.\underset{h0}{lim}[\frac{(3+h{)}^{-2}-3^{-2}}{h}]$

$(4$ marks$)$

b$.\underset{x2}{lim}\frac{x^2+x-6}{x^2-2x}$

$(4$ marks$)$

c$.\underset{x-2}{lim}\frac{3x^2-\sqrt[\phantom{2}]{9x^4+x+2}}{x^3+2x^2}$

$(4$ marks$)$

d$.\underset{x}{lim}\frac{2-3x^2}{6x^2+5}$

$(4$ marks$)$

e$.\underset{x0}{lim}{x}^{4}sin(\frac{1}{2x^2+3x})$