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MHT CET2011MathematicsFunctions

Let f(x+y)=f(x) f(y), x, y R , suppose that f(3)=3 and f^ (0)=11 , then f^ (3) is given by

Options

  1. A22
  2. B44
  3. C28
  4. D33

Correct answer

D. 33

Step-by-step solution

f^ (3)= _ h 0 f(3+h)-f(3) h aligned &= _ h 0 f(3) f(h)-f(3) h f^ (3) &=3 _ h 0 f(h)-1 h aligned [ f(3)=3] Use L'Hospital rule, aligned f^ (3) &=3 _ h 0 f^ (h) 1 &=3 f^ (0) aligned [ f^ (0)=11 ] =3 11=33

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