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Byju's Answer
Standard XII
Mathematics
Substitution Method to Remove Indeterminate Form
limx→∞√x2 + s...
Question
lim
x
→
∞
√
x
2
+
s
i
n
2
x
x
+
c
o
s
x
equals
A
1
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B
0
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C
∞
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D
does not exist
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Solution
The correct option is
A
1
Given,
lim
x
→
∞
⎛
⎜ ⎜
⎝
√
x
2
+
sin
2
(
x
)
x
+
cos
(
x
)
⎞
⎟ ⎟
⎠
dividing by highest denominator power
=
lim
x
→
∞
⎛
⎜ ⎜ ⎜ ⎜
⎝
√
1
+
sin
2
(
x
)
x
2
1
+
cos
(
x
)
x
⎞
⎟ ⎟ ⎟ ⎟
⎠
=
lim
x
→
∞
(
√
1
+
sin
2
(
x
)
x
2
)
lim
x
→
∞
(
1
+
cos
(
x
)
x
)
=
√
1
+
0
1
+
0
=
1
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0
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