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Byju's Answer
Standard XII
Mathematics
Algebra of Limits
The value of ...
Question
The value of
x
l
i
m
−
−
→
∞
x
sin
π
4
x
cos
π
4
x
Open in App
Solution
lim
x
→
∞
x
sin
(
π
4
x
)
cos
(
π
4
x
)
lim
x
→
∞
sin
(
π
4
x
)
cos
(
π
4
x
)
1
x
Let
1
x
=
t
then as
x
→
∞
,
t
→
0
∴
lim
t
→
0
2
sin
(
π
t
4
)
.
cos
(
π
t
4
)
2
t
lim
t
→
0
sin
π
t
2
2
t
We know that
lim
x
→
0
sin
x
x
=
1
Using this ,
lim
t
→
0
sin
(
π
2
)
t
2
t
=
lim
t
→
0
sin
(
π
2
)
t
2
(
π
2
t
)
.
(
2
π
)
=
π
4
lim
t
→
0
sin
(
π
2
t
)
π
t
2
=
π
4
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