EnglishPGT-2013 UP PCS (Pre) 2007, 2004
Q41.Let f(x) = 2 (1 x) and g(x) 1 x; 1 x 1. Then Rolle’s theorem is
Correct answer: Applicable to both f(x) and g(x)
Q42.The value of c in the Lagrange’s mean value theorem
Correct answer: a b/2
Q43.If f(x) = Ax2 +Bx+C, where A, B, C are constants and A ≠ 0, then in the Lagrange's mean value theorem f(b) – f(a) = (b–a) f'(λ) the value of λ is:
Correct answer: a b 2 +
Q44.The interval in which Lagrange's mean value theorem is applicable, for the function ≠ 1 f(x) =,x 0 f(0) = 0 x
Correct answer: [0.01, 1]
Q45.If f(x) ≤ 2 x +1,0 x 1 = 3- x,1 < x 2, then Rolle's theorem in [0, 2] is
Correct answer: not applicable to this function