Florida B.E.S.T. MA.912.C.1.7

MathGrades 9–12Develop an understanding for limits and continuity. Determine limits and continuity.

The Standard

Find special limits by using the Squeeze Theorem or algebraic manipulation.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students evaluate indeterminate limits by factoring, rationalizing, combining fractions, or applying the Squeeze Theorem. They justify why the transformed expression or bounding functions give the limit.
What Mastery Looks Like: A student recognizes when to factor, rationalize, combine fractions, or squeeze. They show valid steps, find the limit, and explain why substitution becomes possible or why the bounds work.
Common Misconceptions: Students may treat 0/0 as the limit instead of an indeterminate form. They may cancel terms that are not factors or use squeezing when the bounds approach different values.
How to Assess It: Exit ticket: evaluate lim x→0 of x²sin(1/x) and lim x→2 of (x²−4)/(x−2). Name the method used for each.

Lesson moves

On grid paper, place yarn along y=|x| and y=−|x|, then sketch y=xsin(1/x) trapped between them near zero.
Write and defend an answer: Why can a common factor be canceled near a point where the original expression is undefined?
Race to sort limit cards into factor, rationalize, common denominator, or squeeze, then solve one card from each pile.
Use s(t)=16t² to find instantaneous speed at t=3 from an average-speed limit, then explain the canceled factor.

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