AP Calculus BC Monday, 31 August 2015 OBJECTIVE TSW find infinite limits FORM DUE (only if it is...
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Transcript of AP Calculus BC Monday, 31 August 2015 OBJECTIVE TSW find infinite limits FORM DUE (only if it is...
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AP Calculus BCMonday, 31 August 2015
• OBJECTIVE TSW find infinite limits
• FORM DUE (only if it is signed)– Information Sheet (wire basket)
• If you have t-shirt money, bring it up after the beginning bell.
• QUIZ: Sec. 2.2 – 2.4, Trigonometric Review is tomorrow, Tuesday, 01 September 2015.– Pick up (ungraded) assignments on the front table if you
want to use them to study for the quiz.– If you pick them up today, you will turn them in tomorrow.
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Sec. 2.4: Infinite Limits
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Sec. 2.4: Infinite Limits
1
1lim1x x
1
1lim1x x
1
1lim DNE1x x
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Sec. 2.4: Infinite Limits
1
1lim1x x
1
1lim1x x
1
1lim1x x
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Sec. 2.4: Infinite Limits
1
1lim1x x
1
1lim1x x
1
1 DN1
Elim x x
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Sec. 2.4: Infinite Limits
21
1lim1x x
21
1lim1x x
21
1lim1x x
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Sec. 2.4: Infinite Limits
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Sec. 2.4: Infinite Limits
In other words, when x = c, and then there is a vertical asymptote at x = c.
#0
,h c
# other than 0
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Sec. 2.4: Infinite Limits
Ex: Determine all vertical asymptotes.
2) 1
1a f x
x
110
f
At x = –1, numerator ≠ 0 and denominator = 0, VA @ x = –1
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Sec. 2.4: Infinite Limits
Ex: Determine all vertical asymptotes.
210
g
At x = –1 and x = 1, numerator ≠ 0 and denominator = 0, VA @ x = –1 and x = 1
2
2) 1 1
b xg xx
210
g
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Sec. 2.4: Infinite Limits
Ex: Determine all vertical asymptotes.
10
h
At x = (and all multiples of ), numerator ≠ 0 and denominator = 0, VA @ x = k, k є
o) cc th x x cossin
xh xx
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Sec. 2.4: Infinite Limits
Ex: Determine all vertical asymptotes.
820
h
At x = −2, numerator ≠ 0 and denominator = 0, VA @ x = −2
2
22 8d
4) x xh x
x
020
h
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Sec. 2.4: Infinite Limits
Ex: Determine the limit.2
1
3lim1x
x xx
210
f so the function has a VA @ x = 1
1
~ 2lim
~ 1 1x
20
A negative # getting smaller2
1
3lim1x
x xx
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Sec. 2.4: Infinite Limits
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Sec. 2.4: Infinite Limits
Ex: Determine the limit.
20
1 lim 1a)x x
01lim 1
x
20
1limx x
20
1lim 1x x
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Sec. 2.4: Infinite Limits
Ex: Determine the limit.2
1
1 limco
bt
)x
xx
2
12lim 1
xx
1lim cot
xx
2
1
1limcot
0x
xx
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Sec. 2.4: Infinite Limits
Ex: Determine the limit.
0 lim c tc) 3 o
xx
0l m 3 3i
x
0lim cot
xx
0lim 3cot
xx