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AP EAMCET202315 May 2023Morning ShiftMathematicsContinuity and DifferentiabilityActual

If f(x)= array cl 1+6 x-3 x^2, & x 1 x+ ₂ (b^2+7 ), & x>1 array . is continuous at all real x , then b=

Options

  1. A1
  2. B0
  3. C5
  4. D2

Correct answer

A. 1

Step-by-step solution

f(x)= cases 1+6 x-3 x^2, & x 1 x+ ₂ (b^2+7 ), & x>1 cases Since f(x) is continuous at x=1 , Hence aligned & _ h 0 (1+h)=f(1) & _ h 0 [(1+h)+ ₂ (b^2+7 ) ]=1+6-3 & ₂ (b^2+7 )=3 b= 1 aligned

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