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Assignment II* Sayyid Mohammed Hasan February 14, 2014 * Last date for submission 3 March 2014, within class timings. 1 Prob 1 Find the intervals in which f (x) = |x-2| x2 is strictly increasing and strictly decreasing. Prob 2 Evaluate the limit: lim n?8 1 sec2 n2 1 n2 + 2 sec2 n2 4 n2 + ... + 1 sec2 1 n Prob 3 Find the Integral: sin8 x - cos8 x dx 1 - 2 sin2 x cos2 x Prob 4 Discuss the Application and conclusion of Lagranges’s Mean Value Theorem on the function f (x) = |x| on interval [-1, 1]. Prob 5 If y = sin-1 x + sin-1 v 1 - x2 then find dy dx . Prob 6 Find the value of log3 log3 log9 729 + 3 logv3 3. Prob 7 Find the maximum value of the function f (x) = 1 + 2 sin x + 3 cos2 x , 0 = x = 2p/3. Prob 8 Find the minimum value of f (x) = x2 -x+1 x2 +x+1 . Prob 9 For what values of a and b lim x?8 x2 + 1 - ax - b x+1 = 0. Prob 10 Find the Integral: 1 2 x3 2 + x3 1 4 dx ***********END********** 1

Assignment II*
Sayyid Mohammed Hasan
February 14, 2014
* Last
date for submission 3 March 2014, within class timings.
1
Prob 1
Find the intervals in which f (x) =
|x-2|
x2
is strictly increasing and strictly decreasing.
Prob 2
Evaluate the limit:
lim
n?8
1
sec2
n2
1
n2
+
2
sec2
n2
4
n2
+ ... +
1
sec2 1
n
Prob 3
Find the Integral:
sin8 x - cos8 x
dx
1 - 2 sin2 x cos2 x
Prob 4
Discuss the Application and conclusion of Lagranges’s Mean Value Theorem on the function f (x) = |x| on
interval [-1, 1].
Prob 5
If y = sin-1 x + sin-1
v
1 - x2 then find
dy
dx .
Prob 6
Find the value of log3 log3 log9 729 + 3 logv3 3.
Prob 7
Find the maximum value of the function f (x) = 1 + 2 sin x + 3 cos2 x , 0 = x = 2p/3.
Prob 8
Find the minimum value of f (x) =
x2 -x+1
x2 +x+1 .
Prob 9
For what values of a and b
lim
x?8
x2 + 1
- ax - b
x+1
= 0.
Prob 10
Find the Integral:
1
2
x3 2 + x3
1
4
dx
***********END**********
1

Grade:11

1 Answers

Girish Kadam
askIITians Faculty 14 Points
7 years ago
Dear Student, Please post the question again as the format is not correct. askIITian Faculty

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