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→∞
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
√
1 − x2 then find
dy
dx .
Prob 6
Find the value of log3 log3 log9 729 + 3 log√3 3.
Prob 7
Find the maximum value of the function f (x) = 1 + 2 sin x + 3 cos2 x , 0 ≤ x ≤ 2π/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→∞
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→∞
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
√
1 − x2 then find
dy
dx .
Prob 6
Find the value of log3 log3 log9 729 + 3 log√3 3.
Prob 7
Find the maximum value of the function f (x) = 1 + 2 sin x + 3 cos2 x , 0 ≤ x ≤ 2π/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→∞
x2 + 1
− ax − b
x+1
= 0.
Prob 10
Find the Integral:
1
2
x3 2 + x3
1
4
dx
***********END**********
1
