# How do you find f ' if #f(x)=sin (1/x^2)#?

Putting this together, we get:

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An interesting example related to this one is to consider the piecewise-defined function

Again, let

Certainly, when

But

In other words,

Here's a graph of the function

Pretty amazing, isn't it?!?!

Here a closer view near the origin and also making sure we can still see the blue curve. It's oscillating infinitely often as

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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.

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