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Pune University - FY BSc MATHEMATICS - II, April 2010

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Total No. of Questions : 5] [Total No. of Pages : 4 [3717] - 2 P180 F.Y. B.Sc. MATHEMATICS Calculus (Paper - II) (New Course) Time : 3 Hours] Instructions to the candidates : 1) All questions are compulsory. 2) Figures to the right indicate full marks. [Max. Marks : 80 Q1) Attempt all the subquestions : a) Find the rational number between b) Show that cos n [16] 2 and 3. is divergent. n=0 c) Define Cauchy sequence. d) Find the left hand and right hand limits of the function f(x) at x = 4, where f ( x ) = e) x 4 , x 4. x 4 If the function f : R R is defined as f(x) = 1, if x < C = 1 , if x C then show that f is continuous at x = C. f) ax 1 Evaluate, lim x . x 0 b 1 g) Test whether Rolle s theorem is applicable for the function f(x) = x on [ 1, 1]. h) State Taylor s theorem with Lagrange s form of remainder. P.T.O.

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Additional Info : F.Y. B.Sc. MATHEMATICS : Calculus (Paper - II) (New Course), Pune University
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