Example: 6 | |
Evaluate the following limits:
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Solution: 6 | |
The limit is of the indeterminate form , but can be reduced into a combination of two standard limits as follows:
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Solution: 6-(b) | |
can be expanded as
Hence,
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Solution: 6-(c) | |
The numerator in this limits tends to as because
Evaluating this limit will require a little artifice in the following manner:
Now as so that the numerator in the limit above is of the form where .
What should we do now? Multiply and divide by
We get
From the previous example, it follows that the second limit has the value .
Hence, the overall value for this limit is
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Solution: 6-(d) | |
Factoring the numerator and rationalising the denominator gives.
(We have multiplied and divided by above)
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