# What is the limit of #x(sqrt(x^(2)+1)) # as x approaches infinity?

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The limit

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The limit of x(sqrt(x^(2)+1)) as x approaches infinity is infinity.

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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.

- How do you find the limit of #(ln(x)/sin(πx))# as x approaches 1?
- How do you evaluate the limit #(1/x^2-1/9)/(x-3)# as x approaches #3#?
- How do you find the limit #lim (3-sqrt3^x)/(9-3^x)# as #x->2#?
- How do you find the limit of #[1/(3+x)]- (1/3) ÷ x# as x approaches 0?
- How do you find the limit of #sin((x-1)/(2+x^2)) # as x approaches infinity?

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