Chapter 1 Sec 2 & 3

Question 0

Give an example of a function that approaches a different number from the right side of c than the left side of c

Answer 0

I x I
—–
Lim. x
x ➡ 0

Question 1

What are the common types of behavior associated with the no existence of a limit

Answer 1

1. F(x) approaches a different number from the right side of c than the left side of c.
2. F(x) increases or decreases without bound as x approaches c.
3. F(x) oscillates between two fixed values and x approaches c.

Question 2

Give an example of a function that increases or decreases without bound as x approaches c

Answer 2

1
           ------  
                 2
   Lim     x
 x ➡ 0

Question 3

Give an example of a function that oscillates between two fixed values as x approaches c

Answer 3

1
Sin—–
Lim x
x ➡ 0

Question 4

What does the … Equal? ⛔ Is theta

      Sin⛔
     --------   Lim     ⛔ x➡0

Answer 4

= 1

Question 5

What does …. Equal?

        1 - cos x
        ----------    Lim         x x ➡ 0

Answer 5

= 0

Question 6

What is the first thing you Always always do when evaluating a limit analytically

Answer 6

Try direct substitution

Question 7

If direct substitution doesn’t work what other methods can you try

Answer 7

The factor / cancel method

Rationalize the number

Find a common denominator