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99 Percentile Qs Bank for JEE MainMathematicsLimits

_ x 0 ^2 ( ^4 x ) ^2 x^4 =

Options

  1. A0
  2. B4
  3. C1
  4. D16

Correct answer

B. 4

Step-by-step solution

Given _ x 0 ^2 ( ^4 x ) ^2 x^2 It forms 0 0 indeterminate form, then apply L'Hospital rules. aligned & _ x 0 ^2 ( ^4 x ) ^2 x^4 & _ x 0 2 ( ^4 x ) ^2 ( ^4 x ) 4 ^4 x x 4 ^2 x^3 & _ x 0 ( .2 ( ^4 x ) ^2 ( ^4 x ) ^4 x ) x^2 ) _ x 0 ( x x ) & _ x 0 ( 2 ( ^4 x ) x^2 ) _ x 0 ( ^2 ( ^4 x ) ^4 x ) 1 aligned Again Apply L'Hospital rule, aligned & _ x 0 ( 2 ^2 ( ^4 x ) 4 ^4 x x 2 x ) 1 ( ^2 ( ^4 0 ) ^4(0) ) & _ x 0 ( x x ) _ x 0 ( ^2 ( ^4 x ) 4 x ^4 x ) ( ^2( ) 1 ) & 1 ^2 ( ^4(0) ) 4 ^4(0) (-1)^2 & 1 (-1)^2 4 (1)=4 aligned

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