Hemchandracharya North Gujarat University 2002 B.Sc Computer Science 102 : Advance Mathematics - exam paper

______________
(i) lim v four + x +2x2 - 2
x->0 --------------------
X
(ii) lim (1 + x / 1-x )1/x
x->0
(b) explain the continuity of a function 2
F(x) ={ 3x – 2; if x = 0 ,
x +1 ; if x>0
at the point x = 0.


















(c) Evaluate dy/dx if , 6
(i) y = e x - tan x + 3

(ii) y = log(sin x)

(iii) e x + e y = e x+y

OR
(a) (i) describe limit of a function 2

(ii) Evaluate : lim 3x -- 5x two
x->0 ----------
X
(b) explain the continuity of a function 2


F(x) = 3| x | + x2 ; if x ? 0
{ ------------------
two
{ 0 ; if x=0

at point x=0.

(c) (i) If y = e3x + sin x – five then obtain d two y / dx two 2
(ii) If x = a cos ? and y = b sin ? then 2
obtain dy / dx .

Earning:   Approval pending.