# How do you find the limit of # (x)(sin(1/x)) # as x approaches infinity?

Evidently we have:

Thus:

graph{xsin(1/x) [-10, 10, -5, 5]}

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To find the limit of (x)(sin(1/x)) as x approaches infinity, we can use the squeeze theorem. By applying the squeeze theorem, we can establish that the limit is equal to zero.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the limit of #( 1/(x-1) - 2/(x^2-1) )# as x approaches 1?
- What is the limit of lnx-ln(pi)/x-(pi) when x approaches to (pi) from left?
- What is the limit of #(sqrt (9x^6 - x) ) / (x^3 + 4)# as x approaches negative infinity?
- What is the limit of #Abs(sinx) # as x approaches infinity?
- How do you find #lim (x^2-x+4)/(3x^2+2x-3)# as #x->oo#?

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