## 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).

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.