10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;

10/13/2015Mrs. Liu's PreCalc Day192 CP Calculus Block 19 HW p98,x3’s 3-48

10/13/2015Mrs. Liu's PreCalc Day193 Ch 2.4 Continuity and One-sided Limit

10/13/2015Mrs. Liu's PreCalc Day194 Do Now:

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10/13/2015Mrs. Liu's PreCalc Day1910 Objective 1: Determine the continuity of the functions

10/13/2015Mrs. Liu's PreCalc Day1911 Definition A: Continuity at an interior point

10/13/2015Mrs. Liu's PreCalc Day1912 Definition B: Continuity on closed interval [a,b], left endpoint a or right endpoint b

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10/13/2015Mrs. Liu's PreCalc Day1914 Definition C: A function is continuous if it is continuous at each point of its domain

10/13/2015Mrs. Liu's PreCalc Day1915 The Continuity Test The function y=f(x) is continuous at x=c if and only if all of the following are true:

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10/13/2015Mrs. Liu's PreCalc Day1917 Existence of Limit

10/13/2015Mrs. Liu's PreCalc Day1918 Properties of Continuity I Scalar Multiple: bf(x)

10/13/2015Mrs. Liu's PreCalc Day1919 Properties of Continuity ii Sum or difference f + g, or f - g

10/13/2015Mrs. Liu's PreCalc Day1920 Properties of Continuity iii Product f(x)g(x)

10/13/2015Mrs. Liu's PreCalc Day1921 Properties of Continuity iv Quotient f(x)/g(x)

10/13/2015Mrs. Liu's PreCalc Day1922 Continuity of Composite Functions f(g(x)) or g(f(x))

10/13/2015Mrs. Liu's PreCalc Day1923 Theorem: If f is continuous at c and g is continuous at f©, then the composite g o f is continuous at c.

10/13/2015Mrs. Liu's PreCalc Day1924 Example 0 Given f(x)

10/13/2015Mrs. Liu's PreCalc Day1925 a) Determine a complete graph of f(x)

10/13/2015Mrs. Liu's PreCalc Day1926 b) Is f(x) continuous? Explain. Yes. At all points

10/13/2015Mrs. Liu's PreCalc Day1927 Example 1 Find the points at which the function is not continuous

10/13/2015Mrs. Liu's PreCalc Day1928 Example 2 Find the points at which the function is not continuous

10/13/2015Mrs. Liu's PreCalc Day1929 Example 3 Find the points at which the function is not continuous No discontinuities

10/13/2015Mrs. Liu's PreCalc Day1930 Example 4 Find the points at which the function is not continuous No discontinuities

10/13/2015Mrs. Liu's PreCalc Day1931 Example 5 Find the points at which the function is not continuous x=0

10/13/2015Mrs. Liu's PreCalc Day1932 Example 6 Find the points at which the function is not continuous x<1/3

10/13/2015Mrs. Liu's PreCalc Day1933 Example 7 Find the points at which the function is not continuous No discontinuities

10/13/2015Mrs. Liu's PreCalc Day1934 Example 8 Define g(x) so that g(x)=(x 2 -9)/(x-3) is continuous at x=3 g(3)=6

10/13/2015Mrs. Liu's PreCalc Day1935 Example 9 Define f(1) so that f(x)=(x 3 -1)/(x 2 -1) is continuous at x=1

10/13/2015Mrs. Liu's PreCalc Day1936 Example 10 Given g(x)

10/13/2015Mrs. Liu's PreCalc Day1937 What value should be assigned to b to make g(x) continuous at x=1/2?

10/13/2015Mrs. Liu's PreCalc Day1938 Example 11: Find the limit

10/13/2015Mrs. Liu's PreCalc Day1939 Example 12: Find the limit

10/13/2015Mrs. Liu's PreCalc Day1940 Example 13: Find the vertical asymptote(s) of

10/13/2015Mrs. Liu's PreCalc Day1941 Example 14: Find the vertical asymptote(s) of

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10/13/2015Mrs. Liu's PreCalc Day1943 Example 15: Find the end behavior asymptote(s) of

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10/13/2015Mrs. Liu's PreCalc Day1945 Example 16

10/13/2015Mrs. Liu's PreCalc Day1946 Example 17

10/13/2015Mrs. Liu's PreCalc Day1947 Example 18

10/13/2015Mrs. Liu's PreCalc Day1948 Example 19

10/13/2015Mrs. Liu's PreCalc Day1949 Example 20

10/13/2015Mrs. Liu's PreCalc Day1950 Lesson quiz 1: Given

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10/13/2015Mrs. Liu's PreCalc Day1953 No

10/13/2015Mrs. Liu's PreCalc Day1954 No

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