## Exercises - Limits of sequences - Basic methods

Here you will find problems on limits solved by factoring, problems with
difference of roots,
indeterminate ratios,
indeterminate products,
indeterminate powers, and problems that
require
squeezing.

If you want to refer to sections of Methods Survey for limits while working the
exercises, you can click
here and it will appear in a
separate full-size window. Similarly,
here we offer Theory -
Limits.

In the following limit problems, identify the dominant terms in the numerator
and the denominator (see intuitive evaluation). Then use factoring out to find the
limit; in some cases one can also use cancelling.

In the following limits, identify the dominant term and find the limit by
factoring it out. Note that factoring works thanks to the fact that
dominant terms are always unique here.

In the following limit, identify the dominant term in the root and determine
what type of expression the root is. Then factor out the dominant term and find
the limit. Try also cancelling (extending the root to the whole fraction).

Use algebra to get rid of the
difference of roots.

Check that the type of the given problem is the
indeterminate ratio,
then pass to functions and use the L'Hospital rule to find the limit.

Check that type of the given problem is the
indeterminate product.
Then transform the product into a fraction. State the resulting limit that
has to be found and find its type.

Check that the type of the given problem is the
indeterminate power.
Then use the recommended transformation to change the power into a fraction.
State the resulting limit that has to be found and find its type.

Set up the Squeeze theorem for the following limits (see
comparison and
oscillation).

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