Week 2 08/22

Question 1

What does lim f(x) = b mean

Answer 1

It means for every epsilon > 0 there is some delta epsilon > 0 such that for all x
0 > |x-a|< delta epsilon—> |f(x)-b| < epsilon

Question 2

What does f(x) = b
X—> A
Mean

Answer 2

It means the same thing but it can be easier to read and write

Question 3

What does the epsilon-delta definition of a limit describe?

Answer 3

It defines the formal concept of the limit of a function as (x) approaches a value (a). Specifically, it shows that for every (epsilon > 0), there exists a (delta > 0) such that if (0 < |x - a| < \delta), then|f(x) - L| < epsilon).

Question 4

Answer 4

Question 5

Answer 5

Question 6

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

Answer 9

Question 10

Answer 10

Question 11

Answer 11

Question 12

Answer 12

Question 13

Answer 13

Question 14

Answer 14

Question 15

Answer 15

Question 16

Answer 16

Question 17

Question 18

Answer 18

False. The limit (if exists) depends on values of f near a, but it does not depend on the value of f(a).

Question 19

Answer 19

H(4) = 8

Question 20

Use the graph of in the given figure to find the following values, if they exist.

B lim h(x) x—> 4

Answer 20

Lim h(x) x—> 4 = 6

Question 21

Question C) h(8) what is it’s value and if it’s undefined answer why.

Answer 21

It is undefined due to it having an open circle which means that h(8)s value is not defined.

Question 22

Question D) lim h(x) x—> 7 =?

Answer 22

Lim h(x) x—> 7 = 3

Question 23

Find lim h(x) x—> 8. Answer wether does the limit exist and if so what is it

Answer 23

It does have a limit and it is
lim h(x) x—> 8 = 4

Question 24

Answer 24

Question 25

Answer 25

Question 26

Find f(3)

Answer 26

F(3) = 5

Question 27

Find lim f(x) x—> 3-

Answer 27

Lim f(x) x—> 3- = 4

Question 28

Find lim f(x) x—> 3+

Answer 28

Lim f(x) x—> 3+ = 4

Question 29

Find lim f(x) x—> 3

Answer 29

Lim f(x) x—> 3 = 4

Question 30

Find the value of f(5)

Answer 30

F(5) = 4

Question 31

Find lim f(x) x—> 5-

Answer 31

The answer is lim f(x) x—> 5- = 6
Remember to pay attention to which side it’s coming from. It isn’t 3 because there isn’t any lines coming from the left side to 3 but there is one for 6. That is why lim f(x) x—> 5- = 6

Question 32

What is the limit of a variable that comes from both side but when approached from only one side of the graph ( such as the left hand side) isn’t not the same limit as the other ( the right hand side) ?

Answer 32

This means that the limit doesn’t exist for it. Ex: if the limit of x—> 3- is 1 and x—> 3+ is 3 then the limit of x—> 3 doesn’t exist. The opposite is also true. If the limit of x—> 4- is 4 and the limit of x—> 4+ is also 4, then the limit of x—> 4 is 4.

Question 33

What are one sided limits?

Answer 33

A one-sided limit is the value that a function approaches as the input gets close to a specific point, but only from one direction either from the left or from the right.

Question 34

Answer 34

Question 35

Answer 35

Question 36

Answer 36

Question 37

Answer 37