Limit of a Vector Function: Example 2

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Find .

How do we proceed?

We find the limit of each component of the vector.

Set that up.

Evaluate

We are finding the limit of the function as t approaches 2. Do you see any potential difficulty?

Yes, the function is not defined at .

When we find the limit of this function, do we need to consider t being equal to 2?

No, the definition of a limit concerns the value of this function as t approaches 2.

Can we then divide out of both the numerator and denominator?

Yes.

Do that.

We get

Evaluate the second term in the original problem,

Evaluate the third term in the original problem,

Combine these results to express the requested limit.

We get

If the problem had been stated as
,
how would we handle it?

In the same way: by finding the limits of each component.

State the result in this notation.

The end. If you found this helpful and would recommend that I create more pages like this one, please let me know: Email to John Taylor

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