MTH301 Final Term Past Paper Spring 2005

MTH301 Calculus · Final Term Examination – Spring 2005 · Time Allowed: 150 Minutes

1-Duration of the paper is 150 minutes and use of calculator is allowed

4- Pasting the equations of math type from word file into software may cause some visibility problem, so please note that do not copy equations of math type into software from word file. Paste the equations from math type directly into software.

Total Questions: 12

Q1. Marks : 08

Evaluate the iterated integral

(1 · {( , ) :0 · 1, · 3}

R

x · x dA · R · x y · x · y

Q2. Marks : 06

Find the directional derivative (2,0) u Df r of f xy x xy y in the direction

of ui j r at the point (-2, 0).

Q3. Marks : 05

Find the centre and radius of the sphere x y z x y z

Q4. Marks : 02

Let

a · i · j · r

and

b · i · j · r

,then

o

a and b r r are orthogonal

o

The angle b en etwe a and b r r is 4 π

o

a and b r r are parallel.

o

The angle between a and b r r is 6 π

Q5. Marks : 02

The Laplace transform of is

2 t · e · o

if s s

o

if s s

o

if s s

o

2 if s s

Q6. Marks : 02

If (4, 3 π ,- 4) is a point in the Cylindrical coordinates then the same point in Rectangular coordinates is given by

o

(2,2 3 ,4)

o

(2,2 3 ,4)

o

(2,2 3 ,-4)

o

(- 2,2 3 ,4)

o

(2 3 ,2,-4)

Q7. Marks : 02

The differential is an exact differential if we have dz Mdx Ndy

o

M N y y

o

M N y x

o

M N x y

o

M N x x

Q8. Marks : 10

Compute Curl and Divergence for the given vector field F xi xy j yxk u r

Q9. Marks : 02

The function is

yx=

o

Even function

o

Odd function

o

o

Constant Neither even nor odd