Solve the following Question.(1 Marks)

Question 11 Mark

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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Question 21 Mark

Examine whether the function is continuous at the points indicated against them. $f(x)=x^3-2 x+1$, for $x \leq 2$ $=3 x-2$, for $x>2$, at $x=2$

Answer

$
\begin{aligned}
\lim _{x \rightarrow 2^{-}} \mathrm{f}(x) & =\lim _{x \rightarrow 2^{-}}\left(x^3-2 x+1\right) \\
& =(2)^3-2(2)+1=5 \\
\lim _{x \rightarrow 2^{+}} \mathrm{f}(x) & =\lim _{x \rightarrow 2^{+}}(3 x-2) \\
& =3(2)-2=4 \\
\lim _{x \rightarrow 2^{-}} \mathrm{f}(x) & \neq \lim _{x \rightarrow 2^{+}} \mathrm{f}(x)
\end{aligned}
$
$\therefore$ Function $\mathrm{f}$ is discontinuous at $\mathrm{x}=2$

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Question 31 Mark

Examine the continuity of : $\mathrm{f}(\mathrm{x})=\frac{x^2-9}{x-3}$ on $\mathrm{R}$

Answer

$
f(x)=\frac{x^2-9}{x-3} ; x \in R
$
$f(x)$ is a rational function and is continuous for all $x \in R$, except at the points where denominator becomes zero.
Here, denominator $x-3=0$ when $x=3$.
$\therefore$ Function $\mathrm{f}$ is continuous for all $\mathrm{x} \in \mathrm{R}$, except at $\mathrm{x}=3$, where it is not defined.

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Question 41 Mark

Examine the continuity of : f(x)=x^3+2 x^2-x-2 \text { at } x=-2

Answer

$
f(x)=x^3+2 x^2-x-2
$
Here $f(x)$ is a polynomial function and hence it is continuous for all $x \in R$. $\therefore \mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=-2$

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Maths (commerce) Solve the following Question.(1 Marks)

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