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Stuck here, help me understand: - Limit , continuity and differentiability - JEE Main-7

If limit of  f(x)= \frac{x^{2}-k^{2}}{x-k} when x approaches K is 12 then 'k' equals 

  • Option 1)

    2

  • Option 2)

    4

  • Option 3)

    6

  • Option 4)

    8

 
Answers (1)
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As we have learned

Limit C definition -

\lim_{x\rightarrow c}f(x)=l

The  number  l is referred to as the limit of f(x) as  x tends to  a

-

 

 According to given condition 

\lim_{x\rightarrow k} \frac{x^{2}-k^{2}}{x-k}=12 

\Rightarrow \lim_{x\rightarrow k} \frac{(x-k)(x+k)}{x-k}=12

\Rightarrow 2k=12\Rightarrow k=6

 

 

 

 


Option 1)

2

Option 2)

4

Option 3)

6

Option 4)

8

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