Chapter 2 Limit definitions/laws & names

Question 1

How do we express a limit (write it out)?

Answer 1

Lim f(x)
x-->a

Question 2

How do we express a limit from the left or right (write it out)?

Answer 2

lim f(x)    
x-->a ^+/-

Question 3

What does it mean when a limit exists?

Answer 3

1: lim f(x) = lim f(x)
x–>a^- x–>a^+
2: f(a) exists
3:

Question 4

What is a Jump discontinuity ?

Answer 4

Both one-sided limits exist, but have different values. Looks like a jump on the graph up or down.

Question 5

What is a Infinite discontinuity?

Answer 5

Both one-sided limits are infinite. A point on the graph that stretches vertically , infinitely closer to a point but never touching

Question 6

What is a removable discontinuity?

Answer 6

a point on the graph that is undefined or does not fit the rest of the graph. There is a gap at that location when you are looking at the graph.

Question 7

lim (f(x) +/- g(x)) ?

x–>a

Answer 7

Lim f(x) +/-  lim g(x)
x-->a          x-->a

Question 8

lim (f(x) g(x))

x–>a

Answer 8

lim f(x)   times  lim g(x)
x-->a                 x-->a

Question 9

lim (f(x)/g(x))

x–>a

Answer 9

lim f(x) divided by lim g(x)      , as long as lim g(x)
x-->a                      x-->a                              x-->a does not = 0