Maths (commerce) Solve the Following Question.(5 Marks)

Find k if following functions are continuous at the points indicated against them.

\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}

Find k if following functions are continuous at the points indicated against them.

\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}

\begin{aligned}
& f(x)=\frac{\sqrt{x+3}-2}{x^3-1} \text { for } x \neq 1 \\
& =2 \text { for } x=1, \text { at } x=1
\end{aligned}

Test the continuity of the following functions at the points indicated against them.

\begin{aligned}
\mathrm{f}(\mathrm{x})=\frac{x^3-8}{\sqrt{x+2}-\sqrt{3 x-2}} \text { for } \mathrm{x} \neq 2 \\
=-24 \text { for } \mathrm{x}=2, \text { at } \mathrm{x}=2
\end{aligned}