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Problem
Problem
Match the statements of Column I with values of Column II.
Column I
Column II
(A)
lim
x
→
π
+
2
tan
−
1
(
tan
x
)
\lim_{x \to \frac{\pi^+}{2}} \tan^{-1}(\tan x)
lim
x
→
2
π
+
tan
−
1
(
tan
x
)
(p) 0
(B)
lim
n
→
∞
[
∑
r
=
1
n
1
2
r
]
\lim_{n \to \infty} \left[ \sum_{r=1}^{n} \frac{1}{2^r} \right]
lim
n
→
∞
[
∑
r
=
1
n
2
r
1
]
([·] denotes the greatest integer function)
(q) Doesn't exist
(C)
lim
x
→
∞
sec
−
1
(
x
x
+
1
)
\lim_{x \to \infty} \sec^{-1} \left( \frac{x}{x+1} \right)
lim
x
→
∞
sec
−
1
(
x
+
1
x
)
(r)
−
π
2
-\frac{\pi}{2}
−
2
π
(D)
lim
x
→
π
2
−
cos
x
(
1
−
sin
x
)
2
/
3
\lim_{x \to \frac{\pi}{2}^-} \frac{\cos x}{(1 - \sin x)^{2/3}}
lim
x
→
2
π
−
(
1
−
s
i
n
x
)
2/3
c
o
s
x
(s)
π
2
\frac{\pi}{2}
2
π
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