MM

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86

Problem 82

Proof Consider the line $f(x)=m x+b,$ where $m \neq 0 .$ Use the $\varepsilon$ -\delta definition of limit to prove that $$\lim _{x \rightarrow c} f(x)=m c+b$$

Answer

Check back soon!

You must be logged in to like a video.

You must be logged in to bookmark a video.

## Discussion

## Video Transcript

and this problem, we want to show that the limit has X approaches. C of the function f of X equals MX plus B, where M is non zero is equal to M C plus B and we want to do this using that sound out a definition of the limit. So that means we have to show that for each up Floren greater than zero. There is a Delta created in Sarah such that this absolute value, the absolutely of after lex minus and secrets be is less than epsilon whenever if the absolute value of excellent sea is in between zero and daughter. So we want to find the appropriate daughter that will make this work. So first, let's no that the absolute value of f of X minus m c plus B when we were kind of right that out by replacing a vex with its definition is equal to a Mex plus B minus M c plus B quantity. Now only simplify this out. This gives us annex minus emcee since you'll distribute this negative sign to M C and B, and the beans will cancel out nicely there. So then you noticed that both of these terms here has an M factor so we can write this out, factoring out the end. So this will be the absolute value of M times X minus c and then one more step. Buy properties of absolute values. We're multiplying two things inside of an absolutely sign we can kind of split them up into a product about so values. So that will be equal to the absolute I them terms the absolute value of Excellency. So now we have a relationship between this quantity here and this quantity here. So what? We can do this. Let Delta equal Absalon divided by the absolute value them this way, when Delta takes this value, our backs Linus M C plus B is less than absolute, and then we're done.

## Recommended Questions