D 10668 (Pages : 3) வாரி? அவைத்‌ வைக

FIFTH SEMESTER U.G. DEGREE EXAMINATION, NOVEMBER 2021
(CBCSS—UG)
Mathematics
MTS 5B 07—NUMERICAL ANALYSIS
(2019 Admissions)
Time : Two Hours Maximum : 60 Marks
Section A

Answer at least eight questions.
Each question carries 3 marks.
All questions can be attended.

Overall Ceiling 24.

1. Show that f (x) = x° + 4%?—10=0 has a root in [1, 2].
2. Determine fixed points of the function g (x) = x?- 2.
3. Write the equation of Lagrange’s interpolating polynomial through (xp, v9) and (x, 4).

4. State three point end point formula of differentiation.

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5. Using Trapezoidal rule find J, x? dx.

6. Show that f (¢, y) = ¢t|y| satisfies a Lipschitz condition on the interval D = {(¢, y)/1 <= t < 2 and
-83 > ‏'ن‎ > 4

7. Define a convex set.

8. For all x > —1 and any positive m show that 0 < (1+x)” < e”™.

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9. When is the initial value problem a =f(ty), a
10. What is the degree of accuracy or precision of a quadrature formula ?

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