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Grade 12Differential Calculus

lim of sinxx when x tends to infinite.

Profile image of Mostafijur Rahaman
11 Years agoGrade 12
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1 Answer

Profile image of Jitender Singh
11 Years ago
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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.