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Let f(x)= \frac{x^{2}-9}{x-3}\forall ; x\neq 3 , then the value of f(3) for f(x) to be continued at x= 3 will be

  • Option 1)

    3

  • Option 2)

    6

  • Option 3)

    9

  • Option 4)

    12

 

Answers (1)

best_answer

As we have learned

Continuity at a point -

A function f(x)  is said to be continuous at  x = a in its domain if 

1.  f(a) is defined  : at  x = a.

2. \lim_{x\rightarrow a}\:f(x)\:exists\:means\:limit\:x\rightarrow a

of  f(x) at  x = a exists from left and right.

3. \lim_{x\rightarrow a}\:f(x)=f(a)\:then\:the\:limit\:equals \:the\:value\:at\:x=a

-

 

 for continuity at x= 3 ,\lim_{x\rightarrow 3}f(x)=f(3)

\Rightarrow \lim_{x\rightarrow 3}\frac{x^{2}-9}{x-3}=f(3)

\Rightarrow f(3)= \lim_{x\rightarrow 3}\frac{(x-3)(x+3)}{x-3}=6

 

 

 

 


Option 1)

3

Option 2)

6

Option 3)

9

Option 4)

12

Posted by

Himanshu

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