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  • Solve it, Which of the following graphs shows thatlimit exits at x=1 ?

Which of the following graphs shows that limit exits at x=1 ? 

  • Option 1)

  • Option 2)

  • Option 3)

  • Option 4)

 

Answers (1)

best_answer

As we have learned

Geometrical interpretation of continuity of a point -

When a graph breaks at a particular point then it approaches from left and right.

\because \lim_{x\rightarrow a^{-}}\:f(x)=\lim_{x\rightarrow a^{+}}\:f(x)

So limit exist but not continuous: but when it is equal to x = a then f(x) is continuous.
 

\lim_{x\rightarrow a^{-}}\:f(x)=\lim_{x\rightarrow a^{+}}\:f(x)=\lim_{x\rightarrow a}\:f(x)

- wherein

   

 

 In (A)\rightarrow LHL =1, RHL=2  so limit doesn't exist 

 In (B)\rightarrow LHL =1, RHL=2  so limit doesn't exist 

 In (C)\rightarrow LHL =1= RHL  so limit exist 

 In (D)\rightarrow LHL =2, RHL=1  so limit doesn't exist 

 

 

 

 

 

 


Option 1)

Option 2)

Option 3)

Option 4)

Posted by

Himanshu

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