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  • Please Solve RD Sharma Class 12 Chapter Continuity Exercise 8.1 Question 8 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Continuity Exercise 8.1 Question 8 Maths Textbook Solution.

Answers (1)

Answer:

                x=0  (Discontinuous)

Hint:

 For a function to be continuous at a point, its LHL RHL and value at that point should be equal.

Solution:

Given,

f(x)=\left\{\begin{array}{l} \frac{x-x}{2}, x>0 \\\\ \frac{x+x}{2}, x<0 \\\\ 2, x=0 \end{array}\right.      

f(x)=\left\{\begin{array}{l} 0, x>0 \\ x, x<0 \\ 2, x=0 \end{array}\right.

We observe,

[LHL at x=0 ]

                \lim _{x \rightarrow 0^{-}} f(x)=\lim _{h \rightarrow 0} f(0-h)=\lim _{h \rightarrow 0} f(-h)=0

[RHL at x=0 ]

                \lim _{x \rightarrow 0^{+}} f(x)=\lim _{h \rightarrow 0} f(0+h)=\lim _{h \rightarrow 0} f(h)=0

And f\left ( 0 \right )=2

                \lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{+}} f(x) \neq f(0)

Thus,  f\left ( x \right ) is discontinuous at x=0.

 

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