Download PTU B.Sc CS-IT 2020 March 1st Sem 70879 Calculus Question Paper

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Roll No. Total No. of Pages : 02

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have to attempt any FOUR questions.

SECTION-A

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1. Write briefly :
   1. What is Right hand limit & Left hand limit?
   2. State algebra of limits.
   3. Differentiate v(cosh^-1x - 1), (x?0).
   4. Define uniform continuity.
   5. Define absolute values.

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   6. State Leibnitz theorem.
   7. Test the curve y = x⁴ for points of inflexion.
   8. Find asymptotes of the curve y log x = a.
   9. State Maclaurin’s theorem with various form of remainder.
   10. Find lim_x?8(1+1/n)ⁿ

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SECTION-B

2. State and prove theorem on uniqueness of a limit.
3. State and prove maximum and minimum values theorem.

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4. State and prove intermediate value theorem.
5. 1. Examine for convex upwards and point of inflexion of the curve y = x⁴ - 2x² + 1.
   2. If y = sin^-1x cos 4x, find y_n.
6. 1. Find all the asymptotes of the curve x³ — 3x² + xy =0.

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   2. If y= (sin^-1x)², then show that (1 — x²) y₂ — xy₁ = 2. Hence or otherwise prove that (1-x²) y_n+2—(2n+ 1) xy_n+1—n²y_n =0
7. Trace the curve y=x/(x—1).

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