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

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