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  • Please Solve RD Sharma Class 12 Chapter 8 Continuity Exercise 8.1 Question 15 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 8 Continuity Exercise 8.1 Question 15 Maths Textbook Solution.

Answers (1)

Answer:

                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} x, \text { if } x>0 \\\\ 1, \text { if } x=0 \\\\ -x, \text { if } 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)=\lim _{h \rightarrow 0}-(-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 )=1

                \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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