$1.$Find the limit$(4\%+5\%+6\%$

$(1)$ Find the limit of each function $($a$)$ as $x$ and $($b$)$ as $x-.$

$g(x)=\frac{1}{8-(\frac{5}{x^2})}$

$(2)\underset{x{2}^{-}}{lim}\frac{3}{x-2}$

$(3)\underset{t0}{lim}\frac{2t}{tant}$At what points are the functions continuous? $(10\%)$

$y=\frac{x+3}{x^2-3x-10}$

$3.$Find the slope of the curve at the point indicated. $(10\%)$

$y=5x^2,x=-1$

$(1)$ Find the derivatives of the function. Then find the values of the derivatives as specified$(10\%)$

$F(x)=(x-1{)}^2+1$;$F^{\text{'}}(-1),F^{\text{'}}(0),F^{\text{'}}(2)$

$(2)$Find the derivative of the function$(10\%)$

$r=sin+cos$

Find an equation for the line tangent to the curve at the point defined by the given value of $t.$ Also, value of $\frac{d^{2}y}{d{x}^2}$ at this point. $(10\%)$

$x=2cost,y=2sin,t=\frac{}{4}$

Find the function's absolute maximum and minimum values and say where they are assumed. $(10\%)$

$f()={}^{\frac{3}{5}},-32x1$

Evaluate the integrals$(5\%+10\%)$

$(1){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\frac{\sqrt[\phantom{2}]{x}}{2}+\frac{2}{\sqrt[\phantom{2}]{x}})dx$

$(2){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{3dx}{(2-x{)}^2}$

Evaluate the integrals$(10\%)$

${\displaystyle \underset{-3}{\overset{4}{}}}(5-\frac{x}{2})dx$