Introduction to the concept of limits

Explain what it means for a function to have a limit as x approaches a given value

Estimate a limit numerically by completing a table of function values approaching a point from both sides

Find a limit analytically using direct substitution, then factoring and simplifying if the result is undefined

Determine when a limit does not exist, including cases where left- and right-hand limits diverge to positive and negative infinity

Have students complete the blank table of values on their own calculators before revealing the completed table on the following slide, since the deck's own build separates the blank and completed versions

Work through the three analytical examples in order, since each introduces one more step of the three-step method than the last

Pair the third example's graph with a discussion of one-sided limits, since it is the deck's only example where the limit does not exist

Numerical limit estimation — students complete a table of function values on both sides of a point using a calculator and read off the limit.

Algebraic limit evaluation — students apply direct substitution and factoring to evaluate limits of rational functions.

Limit non-existence reasoning — students use one-sided behavior (approaching positive or negative infinity) to conclude when a limit does not exist.