# Evaluate the limit? # lim_(x rarr 0) x^2sin(1/x) #

# lim_(x rarr 0) x^2sin(1/x) = 0#

We want to find:

graph{x^2sin(1/x) [-0.3268, 0.3302, -0.1632, 0.1654]}

So then, the limit can be written:

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The limit of x^2sin(1/x) as x approaches 0 is 0.

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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+2x)^(1/x)# as x approaches infinity?
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- How do you find the limit #((1-x)^(1/4)-1)/x# as #x->0#?
- How do you prove that the limit of #((9-4x^2)/(3+2x))=6# as x approaches -1.5 using the epsilon delta proof?
- How do you evaluate #((2x-1)/(2x+5))^(2x+3)# as x approaches infinity?

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