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lim of sinx x when x tends to infinite.

lim of sinxx when x tends to infinite.

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

Function in the limit is not clear.
If the function is
f(x) = sin (x)^{x}
\lim_{x\rightarrow \infty } sin (x)^{x}
Limit is not determinate.
Because we have sin of some number which is closer to infinity is not determinable.

If the function is
f(x) = (sin x)^{x}
\lim_{x\rightarrow \infty }(sin x)^{x}
Then also the limit is not determinable.
Because we cant determine infinity.
For example,
If we have sin of infinity is 1 & -1. Then limit is 1 & -1 respectively.
If we have sin of infinity is b/w -1 & 1. Then limit is 0.

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