Bell Ringer
Find all values of c such that f is continuous on (∞, ∞).
both a and b none of the above
What is the domain of f(x)? x ≠ 0 x ≥ c2 x > c^{2} both a and b none of the above
Find the following limit: given that the function is continuous throughout. 0 ∞ f(0) f(c) none of the above
Find the following limit: ∞ ∞ 1 0  none of the above
Review
 Finding limits using a table
 Finding limits using a graph
 EpsilonDelta Limit Proofs
 Limit Properties
 Dividing Out/Rationalizing Techniques
 Functions that agree at all but one point
 Onesided Limits
 Infinite Limits
Lesson
Find the values of the constants a and b such that
Consider the function Find the domain of f. Calculate Calculate
Determine all values of the constant a such that the following function is continuous for all real numbers.
 Let a be a nonzero constant. Prove that if , then Show by means of an example that a must be nonzero.
Exit Ticket

The function f and its graph are shown below:

Calculate the limit of f(x) as x gets closer to 2 from the left side.

Which value is greater?

the limit of f(x) as x goes to 1

f(1)

Explain your answer.

At what value(s) of c on the interval [0, 4] does the limit of f(x) as x goes to c not exist?

Explain your answer.
 Lesson Objective(s)
 How are the concepts in chapter 1 related and applied?
Standard(s)
 APC.2
 Define and apply the properties of limits of functions.
 Limits will be evaluated graphically and algebraically.
 Includes:
 limits of a constant
 limits of a sum, product, and quotient
 onesided limits
 limits at infinity, infinite limits, and nonexistent limits*
 APC.3
 Use limits to define continuity and determine where a function is continuous or discontinuous.
 Includes:
 continuity in terms of limits
 continuity at a point and over a closed interval
 application of the Intermediate Value Theorem and the Extreme Value Theorem
 geometric understanding and interpretation of continuity and discontinuity
 APC.4
 Investigate asymptotic and unbounded behavior in functions.
 Includes:
 describing and understanding asymptotes in terms of graphical behavior and limits involving infinity
