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Prob 1 If f (x) = x2 1/x2 v sin( t)dt, then find the value of f (1). Prob 2 Let a = min x2 + 4x + 5, x ? R and b = lim??0 1-cos 2? ?2 then find the value of a-b a+b . Prob 3 The value of the Integral Hint: p/2 (ax3 -p/2 cos x + b sin x + c)dx, depends on how many parameters among (a , b , c). Integral of an odd function over the interval [-a,a] is zero.. Prob 4 Find the value of the Integral p/2 -p/2 v ( cos x - cos3 x)dx. Prob 5 Let f (x) = x 0 ( u22u+1 )du then find the least value of f (x) in [-1,1]. -2u+2 Prob 6 Find the values of a for which the function f (x) = cos x - sin x + ax + b is decreasing. Prob 7 Find the area bounded by the curves y = x|x| , x - axis , x = 1 & x = -1. Prob 8 For x > 0 let f (x) = Hint: x ln(t) dt, 1 1+t Find the function f (x) + f (1/x) and show that f (e) + f (1/e) = 1/2. write f(x) and f(1/x) then use substitution to make their limits same.. Prob 9 Is the function f (x) = |x2 - x| differentiable at x = 2. If yes find it’s derivative. Prob 10 Check the monotonicity of f (x) = x sin x in (0, p/2).

Prob 1
If f (x) =
x2
1/x2
v
sin( t)dt, then find the value of f (1).
Prob 2
Let a = min x2 + 4x + 5, x ? R and b = lim??0
1-cos 2?
?2
then find the value of
a-b
a+b .
Prob 3
The value of the Integral
Hint:
p/2
(ax3
-p/2
cos x + b sin x + c)dx, depends on how many parameters among (a , b , c).
Integral of an odd function over the interval [-a,a] is zero..
Prob 4
Find the value of the Integral
p/2
-p/2
v
( cos x - cos3 x)dx.
Prob 5
Let f (x) =
x
0
( u22u+1 )du then find the least value of f (x) in [-1,1].
-2u+2
Prob 6
Find the values of a for which the function f (x) = cos x - sin x + ax + b is decreasing.
Prob 7
Find the area bounded by the curves y = x|x| , x - axis , x = 1 & x = -1.
Prob 8
For x > 0 let f (x) =
Hint:
x ln(t)
dt,
1 1+t
Find the function f (x) + f (1/x) and show that f (e) + f (1/e) = 1/2.
write f(x) and f(1/x) then use substitution to make their limits same..
Prob 9
Is the function f (x) = |x2 - x| differentiable at x = 2. If yes find it’s derivative.
Prob 10
Check the monotonicity of f (x) =
x
sin x
in (0, p/2).

Grade:Upto college level

2 Answers

Girish Kadam
askIITians Faculty 14 Points
7 years ago
Dear Student, Please submit the question again in proper alignment. askIITians faculty
Babi
37 Points
7 years ago
The answer is please guess it

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