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Class 9Class 10First YearSecond Year
$Example 4: Discuss the continuity of the function f(x) and g(x) at x=3 .(a) f(x)=\left\{\begin{array}{cc}\frac{x^{2}-9}{x-3} & \text { if } x \neq 3 \\ 6 & \text { if } x=3\end{array}\right.$

4. Express each limit in terms of e :$\text { (x) } \operatorname{Lim}_{x \rightarrow 0} \frac{e^{1 / x}-1}{e^{1 / x}+1} x<0$

$Example 1:Graph the circle x^{2}+y^{2}=4$

$4. Express each limit in terms of e :(ix) \operatorname{Lim}_{x \rightarrow \infty}\left(\frac{x}{1+x}\right)^{x}$

$1. Evaluate each limit by using theorems of limits:(v) \operatorname{Lim}_{x \rightarrow 2}\left(\sqrt{x^{3}+1}-\sqrt{x^{2}+5}\right)$

Example 1: Determine whether \operatorname{Lim}_{x \rightarrow 2} f(x) and \operatorname{Lim}_{x \rightarrow 4} f(x) exist when$f(x)=\left\{\begin{array}{rcc}2 x+1 & \text { if } & 0 \leq x \leq 2 \\7-x & \text { if } & 2 \leq x \leq 4 \\x & \text { if } & 4 \leq x \leq 6\end{array}\right.$

$Example 7:Evaluate: \operatorname{Lim}_{\theta \rightarrow 0} \frac{1-\cos \theta}{\theta}$