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  • Please Solve RD Sharma Class 12 Chapter 8 Continuity Exercise 8.1 Question 14 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 8 Continuity Exercise 8.1 Question 14 Maths Textbook Solution.

Answers (1)

Answer:

                f\left ( x \right ) is discontinuous at the point x=0

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}{ll} 3 x-2, & \text { if } x \leq 0 \\\\ x+1, & \text { if } x>0 \end{array}\right)     at  x=0

                f(x)=\left(\begin{array}{l} 3 x-2, \text { if } x<0 \\\\ -2, \text { if } x=0 \\\\ x+1, \quad \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} 3(-h)-2=-2

[RHL at x=0 ]            

                \begin{gathered} \lim _{x \rightarrow 0^{+}} f(x)=\lim _{h \rightarrow 0} f(0+h)=\lim _{h \rightarrow 0} f(h)=\lim _{h \rightarrow 0}(h+1)=1 \\\\ \lim _{x \rightarrow 0^{+}} f(x) \neq \lim _{x \rightarrow 0^{-}} f(x) \end{gathered}

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

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