Limits Review (Basic)

1. Evaluating Limits
A Checklist to Use!

2. 1. Always try direct substitution!
• Plug in the specific x-value being approached—if you get a y-
value, that is the limit!
• If you get a value that is undefined (like 8/0), then you will need
to use the graph or the table.
• If you get a value that is indeterminate (like 0/0), then you will
need to move to the next step.

3. 2. Try algebra!
• Common techniques used algebraically are:
• Factoring: divide out common factors and try direct
substitution again
• Rationalizing: simplify the radical expressions and try direct
substitution again
• Common Denominators: simplify the rational expressions and
try direct substitution again

4. 3. Use the graph!
• Look at the graph of the function and see what
y-value it approaches as you get closer and closer
to your x-value.

5. 4. Use the table!
• Look at the table of values of the function and
see what y-value the function approaches as you
get closer and closer to your x-value.

6. Remember that infinite limits are the
exception!
• When x approaches infinity, use end behavior to
help you determine the limit!
• If the degrees of the numerator and denominator are
equal, divide the leading coefficients.
• If the degree of the denominator is larger, the
function is approaching 0.
• If the degree of the numerator is larger, use long
division to identify the slant asymptote.