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Forum  
1. a) Solve the inequality x + x – 1 > 1 5
b)
x
x
Evaluate ^{l im }_{8}x(
1+ x
X:((
2. a) b)  Find the values of a and b so that function differentiable at x = 1 If y = (Tan x)Cot x + (Cot x)Tan x find dy dx .  f (x) =  x3 ax + b  if if  x < 1 x = 1  is continuous and  5 5 
3. a)  A 6 feet tall man is walking towards a lamp post 16 feet high at a speed of 5 ft/sec. At what rate is the tip of shadow moving, at what rate is the length of shadow moving? 5 
d^{n }l nx (1)^{n}
= dx^{n }(
x x
X (:
n! 1 1 1
b) Show
[l nx 1
]
n+1
_{3 }…….
2
n
3
x+y^{3 }
if (x,y) ? (0, 0)
4. a) If f (x, y) = x^{2}+y^{2 }The evaluate f x(0, 0), f y(0, 0) if possible.
(x,y) =(0,0)
0 b) Using mean value theorem to show that Tan x + Tan y = x + y for all real x and y in the interval
_{2 }^{,}_{2}^{[}
ð ð
]
5. a) Find by Maclaurin’s formula the 1^{st }four terms of expansion of f (x) = e ^{ax }Cos bx and write the remainder after n terms.
X
:
1/x 1/x x
a +b
l im
b) Use L’Hospital’s rule to prove that = ab,a>0, b>0
x(
2
5
8
ð
22
xa
6. a) Evaluate ? 4 dx. 5
xb) Evaluate ?sec^{3}x dx. 5
7. a) Integrate the following w.r.t. x
5
3
1 + x
b) Cosx
1 Cosx 5
ð/2

8. a) Show that
ln Sinx dx= _{2}ln2.
1
pq
b) IfIn=? x(1 –x)^{n}dx whereÞ,q,n arepositive.Show(qn + Þ+ 1)In= qn In1.Wherenis+ve integer.
_{*** }B.A/B.ScI (09/A) xxiii _{*** }
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last updated on 28042019 