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  • Solve! - Limit , continuity and differentiability - JEE Main-4

\lim_{x\rightarrow 2}\frac{x^{4}-16}{x-2} equals 

  • Option 1)

    12

  • Option 2)

    24

  • Option 3)

    32

  • Option 4)

    48

 

Answers (1)

best_answer

As we have learned

Evaluation of limits using standard results -

\lim_{x\rightarrow a}\:\frac{{x^{n}}-{a^{n}}}{x-a}=n a^{n-1}

- wherein

\because \:{x^{n}}-{a^{n}}=(x-a)({x}^{n-1}+{x}^{n-2}a +{x}^{n-3}a^{2}+. ......{a}^{n-1})

 

 \lim_{x\rightarrow 2}\frac{x^{4}-16}{x-2}=\lim_{x\rightarrow 2}\frac{x^{4}-2^{4}}{x-2}=4*(2)^{4-1}=32

 

 

 

 


Option 1)

12

Option 2)

24

Option 3)

32

Option 4)

48

Posted by

Himanshu

View full answer

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