BSc Mathematics SEM II ATKT 2016-17 ATKT MATHS I Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q2 Examine convergence of following Attempt any three. [each 4]
2. Q1 Find partial sum and determine if the series converge or diverge
3. Q2 Leibnitz theorem and examine the of
4. Q3 absolute convergence of series and prcve that absolute convergent series are convergent
5. Q4 State Modified root test and examine the convergence of
6. Q2 Attempt any one. [edch 8] ) derivative of a real valued function fat x an open interval-subset of R and show that following functions fare differentiable on R : State theorem and find of
7. Q1 Find y,,n‘" order derivative of y ify =
8. Q2 xy — logy = 1 then prove that + (xy
9. Q3 ind equation of tangent and normal to the fo
10. Q4 If < x <1 then find derivative of y =
11. Q3 any one. [each 8] Verify Rolle’s Theorem for = [0,4 ]
12. Q2 State Lagranges Mean Value Theorem and give their geometrical interpretation, ! Verify Lagranges Mean Value Theorem for f (x) = — 4 in [2,3]
    • (b) any three. [each 4]
13. Q1 Find the Taylor’s Polynomials of degree n at :c = a@ for the mentioned values of L-Hospital’s Rule and evaluate following absolute maximym and minimum values of each function on the given
14. Q4 Divide the number two parts so that the sum of their square is minimum
15. Q4 Attempt any three. [each 5]
16. Q1 Prove that the series converges if p > 1 and diverges if p < 1 rove that the necessary and sufficient conditj on for a series Xa,, to be convergent function f:1 > Ropen interval, is differentiable at c prove that | is continuous at /. What about converse?
17. Q4 Verify Cauchy Mean Value Theorem for f(x) = Vx, g(x) = in
18. Q5 Sketch the graph of y = x? Is F(x) |x| differentiable on R?

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