Examine whether the function is continuous at the points indicated against them $\mathrm{f}(\mathrm{x})=\frac{x^2+18 x-19}{x-1}$ for $\mathrm{x} \neq 1$
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Solve the following Question.(1 Marks)
4 Q→02Solve the Following Question.(2 Marks)
3 Q→03Solve the Following Question.(3 Marks)
2 Q→04Solve the Following Question.(4 Marks)
7 Q→05Solve the Following Question.(5 Marks)
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$
\begin{aligned}
& f(x)=\frac{x^2-9}{x-3}+a, \text { for } x>3 \\
& =5, \text { for } x=3 \\
& =2 x^2+3 x+b, \text { for } x<3
\end{aligned}
$
is continuous at $x=3$
$f(x)=x^2+a$, for $x \geq 0$ $=2 \sqrt{x^2+1}+b$, for $x<0$ and $f(1)=2$, is continuous at $x=0$
\begin{aligned}
& \mathrm{f}(\mathrm{x})=(1+k x)^{\frac{1}{x}}, \text { for } \mathrm{x} \neq 0 \\
& =e^{\frac{3}{2}}, \text { for } \mathrm{x}=0, \text { at } \mathrm{x}=0
\end{aligned}
$
\begin{aligned}
& f(x)=\frac{32^x-1}{8^x-1}+a, \text { for } x>0 \\
& =2, \text { for } x=0 \\
& =x+5-2 b, \text { for } x<0
\end{aligned}
$
is continuous at $x=0$
\begin{aligned}
& f(x)=\frac{45^x-9^x-5^x+1}{\left(k^x-1\right)\left(3^x-1\right)} \text { for } x \neq 0 \\
& =\frac{2}{3} \text { for } x=0, \text { at } x=0
\end{aligned}
\begin{aligned}
& f(x)=\left(\frac{5 x-8}{8-3 x}\right)^{\frac{3}{2 x-4}} \text { for } x \neq 2 \\
& =k \text { for } x=2 \text { at } x=2
\end{aligned}
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