1.6 ContinuityCALCULUS 9/17/14

Warm-up The cost (in dollars) of removing p% of the pollutants from the water in a small lake is given by Where C is the cost and p is the percent of pollutants. A) find the cost of removing 50% of the pollutants B) What percent of the pollutants can be removed for $100,000? C) Evaluate Explain your results

Warm-up (1.6 Continuity-day 2) 1) Find the limit.

2)

1.6 Continuity

What are some examples of continuous functions?

• Polynomials – continuous at every real number

• Rational functions – continuous at every number in its domain

𝑓 (𝑥 )=𝑥2−4𝑥−2

On what interval is this function continuous?

“The function has a discontinuity at c”

Removable and nonremovable discontinuitieso Removable- if can be made continuous by defining at that point

oNonremovable – when the function cannot be made continuous at x=c -Ex. cannot be redefined at x=0

Continuity on a closed interval If is continuous on the open interval (a,b)

Then is continuous on the closed interval [a,b]

𝑓 (𝑥 )=√3−𝑥• Domain:

•Graph

•Continuous

𝑔 (𝑥 )={5−𝑥 ,−1≤ 𝑥≤2𝑥2−1 ,2<𝑥 ≤3Is continuous on a closed intervalClosed endpoints? Continuous on open interval (a,b)?

𝑓 (𝑥 )={ 𝑥+2 ,−1≤𝑥<314−𝑥2 ,3≤ 𝑥≤5

Greatest integer function = greatest integer less than or equal to x

Ex. 5 p. 66

-Sketch the graph and analyze the discontinuities