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AP EAMCET202422 May 2024Evening ShiftMathematicsContinuity and DifferentiabilityActual

If a real valued function f(x)= array cl 2 x^2+(k+2) x+9 3 x^2-7 x-6 & , for x 3 l & , for x=3 array .x=3 and l is a finite value, then l-k=

Options

  1. A31 11
  2. B124 11
  3. C24
  4. D32

Correct answer

B. 124 11

Step-by-step solution

Since, f(x) is continuous at x=3 _ x 3 f(x)=f(3) Now, _ x 3 f(x)= _ x 3 2 x^2+(k+2) x+9 3 x^2-7 x-6 For this limit to exist, we must have aligned & _ x 3 2 x^2+(k+2) x+9=0 & 18+3 k+6+9=0 k=-11 aligned So, _ x 3 2 x^2-9 x+9 3 x^2-7 x-6 = _ x 3 4 x-9 6 x-7 = 3 11 =l Thus, l-k= 3 11 +11= 124 11

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