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COMEDK2024Morning ShiftMathematicsLimitsActual

_ x 0 ( a x b x )^k equals

Options

  1. Ab a
  2. B( b a )^k
  3. C( a b )^k
  4. Da b

Correct answer

C. ( a b )^k

Step-by-step solution

The given limit is L = _ x 0 ( ax bx )^k . We can rewrite the expression inside the limit as: ax bx = ax ax bx bx ax bx Using the standard limit _ 0 = 1 , we have: _ x 0 ax ax = 1 and _ x 0 bx bx = 1 . Therefore, _ x 0 ax bx = _ x 0 ( ax ax bx bx a b ) = 1 1 a b = a b . Applying the power k to the limit: L = ( _ x 0 ax bx )^k = ( a b )^k . Answer: ( a b )^k

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