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.

Sec. 2.4: Infinite Limits

Sec. 2.4: Infinite Limits

1

1lim1x x

1

1lim1x x

1

1lim DNE1x x

Sec. 2.4: Infinite Limits

1

1lim1x x

1

1lim1x x

1

1lim1x x

Sec. 2.4: Infinite Limits

1

1lim1x x

1

1lim1x x

1

1 DN1

Elim x x

Sec. 2.4: Infinite Limits

21

1lim1x x

21

1lim1x x

21

1lim1x x

Sec. 2.4: Infinite Limits

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

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

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

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

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

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

Sec. 2.4: Infinite Limits

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

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

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