Solve the Following Question.(4 Marks)

Question 14 Marks

Find a and b if following functions are continuous at the point indicated against them.

$
\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 $x=0$

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Question 24 Marks

\begin{aligned}
& f(x)=\frac{\log x-\log 3}{x-3} \text { for } x \neq 3 \\
& =3 \text { for } x=3, \text { at } x=3
\end{aligned}

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Question 34 Marks

\begin{aligned}
& f(x)=\frac{3^x+3^{-x}-2}{x^2} \text { for } x \neq 0 \\
& =(\log 3)^2 \text { for } x=0 \text { at } x=0
\end{aligned}

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Question 44 Marks

For what values of $a$ and $b$ is the function
$f(x)=a x+2 b+18 \text { for } x \leq 0$
$=x^2+3 a-b \text { for } 0<x \leq 2=8 x-2 \text { for } x>2, \text { continuous for every } x ?$

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Question 54 Marks

Test the continuity of the following functions at the points indicated against them. $f(x)=\frac{x^3-27}{x^2-9}$ for $0 \leq x<3$ $=\frac{9}{2}$, for $3 \leq x \leq 6$, at $x=3$

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Question 64 Marks

Test the continuity of the following functions at the points indicated against them.$f(x)=4 x+1$ for $x \leq \frac{8}{3}$ $=\frac{59-9 x}{3}$, for $\mathrm{x}>\frac{8}{3}$, at $\mathrm{x}=\frac{8}{3}$

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Question 74 Marks

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

\begin{aligned}
f(x)=\frac{\sqrt{x-1}-(x-1)^{\frac{1}{3}}}{x-2} \text { for } x \neq 2 \\
=\frac{1}{5} \text { for } x=2 \text {, at } x=2
\end{aligned}

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Maths (commerce) Solve the Following Question.(4 Marks)

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