22.

23.

24.
25.

26.

27.

93837

3 C 20645

: (മ്മാ) t fe* dx = 2
Given ffe dx dy = ൩, find the value of 9
R? 0

Show that +p >0,q>0 B(p,q) = ८
൧9

(5 x 6 = 30 marks)
Section C
Answer any two questions.
Each question carries 10 marks.
State and prove Location of roots theorem.

State and prove Additivity theorem.

3 .
Evaluate (a) lim ~ for xeR,x>0. (b) lim sin Nx
1+x" 1+nx

+X

for xe R,x>0.

Discuss about their uniform convergence.

1
(a) Show that ~ >~1, [x7e “dx converges.
0

1
(b) Show that 4 <-1, [27९ “dx diverges.
0

(2x 10 =20 marks)

93837