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PARAGRAPH: Let g(x)= cases a x^2+b x+c ( ^n x ) 4+ ^n x , & x (0, 4 ) 1, & x= 4 x+ x+ ^n x 1+c ( ^n x ) , & x ( 4 , 2 ) cases where a, b, c are real constants, and f(x)= Lim _ n g(x) QUESTION: If f(x) is continuous at x= 4 then c is equal to

Options

  1. A-1
  2. B1
  3. C2
  4. D-2

Correct answer

B. 1

Step-by-step solution

Clearly f ( ⁻ 4 )= c ; f ( ⁺ 4 )= 1 c (i) As Lim _ x 4 f(x) exists, so c= 1 c c= 1 (ii) As f(x) is continuous at x= 4 , so Lim _ x 4 f(x)=f ( 4 ) c= 1 c =1 c=1

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