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Code: 13A54101

B.Tech I Year (R13) Supplementary Examinations December/January 2014/2015

MATHEMATICS ? I

(Common to all branches)

Time: 3 hours Max. Marks: 70

PART ? A

(Compulsory Question)

*****

1 Answer the following: (10 X 02 = 20 Marks)

(a) Solve

(b) Solve .

(c) Expand in a neighborhood of

(d) Find the envelop of the family of curves for different values of

(e) Find the asymptotes of

(f) Find the quadrature of the rectangular hyperbola from

(g)

(h) =

(i) Prove that , is a constant vector.

(j) State Green?s theorem.

PART ? B

(Answer all five units, 5 X 10 = 50 Marks)

UNIT - I

2 The deflection of a strut of length with one end built - in and the other end subjected to the end thrust

satisfies Find the deflection of the strut at a distance from the built - in end.

OR

3 Solve

UNIT - II

4 Verify Maclaurin?s theorem for with Lagrange form of remainder up to 3 terms with

OR

5

Find the radius of curvature at any point on the parabola Show that it is . Where

is the focus of the parabola?

UNIT - III

6 Find the volume of the solid generated by revolution of the loop of the curve about the

OR

7

Evaluate the integral .

UNIT - IV

8

Find the Laplace transform for .

OR

9

The triangular wave function defined by and Find Laplace transform of

UNIT - V

10

Find the directional derivative of in the direction of at the point

OR

11

If evaluate where is the region bounded by the surface

*****

R13

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This post was last modified on 11 September 2020