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MHT CET202014 Oct 2020Morning ShiftMathematicsContinuity and DifferentiabilityActual

If f(x)= (81)^ x -(9)^ x (k)^ x -1 if x 0=2 if x=0 is continuous at x=0 , then the value of k is

Options

  1. A3
  2. B9
  3. C2
  4. D4

Correct answer

A. 3

Step-by-step solution

_ x 0 81^ x -9^ x k^ x -1 =2 _ x 0 9^ x (9^ x -1 ) k^ x -1 =2 ( _ x 0 9^ x ) ( _ x 0 9^ x -1 x ) _ x 0 k^ x -1 x =2 9 k =2 9=2 k k²= 9 k²=9 k=3

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