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  • Need solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 3 subquestion (i)

Need solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 3 subquestion (i)

Answers (1)

Answer:

 x = 1

Hint:

 Show LHS \neq RHS or LHL \neq the value of function at given point or RHL \neq the value of function at given point.

Given:

 f(x)=\left\{\begin{array}{rr} x^{3}-x^{2}+2 x-2 & x \neq 1 \\ 4 & x=1 \end{array}\right.

Explanation:

Now consider the point  x = 1

\begin{aligned} &\text { L.H.L }=\lim _{x \rightarrow 1} f(x)=\lim _{x \rightarrow 1} x^{3}-x^{2}+2 x-2 \\ &=1-1+2 \times 1-2 \\ &=0 \end{aligned}

\begin{aligned} &\text { R.}{\text {H.L }}=\lim _{x \rightarrow 1^{+}} f(x)=\lim _{h \rightarrow 0} f(1+h)=\lim _{h \rightarrow 0}(1+h)^{3}-(1-h)^{2}+2(1+h)-2 \\ &=1-1+2-2=0 \\ &\qquad f(1)=4 \end{aligned}

As

\begin{aligned} &\text { L.H.L } = \text { R.H.L }\neq f(1) \end{aligned}

f(x) is discontinuous at x =1

Posted by

Gurleen Kaur

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