Evaluating Limits Analytically. Lesson 1.3. What Is the Squeeze Theorem?. Today we look at various properties of limits, including the Squeeze Theorem. How do we evaluate limits?. Numerically Construct a table of values. Graphically Draw a graph by hand or use TI’s. Analytically
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Today we look at various properties of limits, including the Squeeze Theorem
Let b and c be real numbers and
let n be a positive integer:
Algebraic Properties of Limits:
Let b and c be real numbers, let n be a positive integer, and let f and g be functions
with the following properties:
Too many to fit on this page….
Sum or Difference:
Let n be a positive integer. The following limit is valid for all c if n is odd, and is valid for all c > 0 if n is even…
If f and g are functions such that…
By now you should have already arrived at the conclusion that many algebraic functions can be evaluated by direct substitution. The six basic trig functions also exhibit this desirable characteristic…
Let c be a real number in the domain of the
given trig function.
for all x on
Use Squeeze Theorem!
Use the squeeze theorem to find:
Direct Substitution doesn’t work.
Rationalize the numerator.
Gap in graph Asymptote