Question

4) Find all values where the function is discontinuous.
f(x) = 4x/((3x-1)(2x+5))

Answer 1

Btw this is just review for my midterm on my week points for calculus.

Answer 2

there are relatively few cardinal sins in math; the biggest is dividing by a zero

Answer 3

So i really appreciate the help, I have been so busy with my senior project and my other class that I have had very little time to study.

Answer 4

what values of x make the bottom go zero?

Answer 5

Finding the zero's?

Answer 6

the zeros of the bottom, not the zeros of the function perse

Answer 7

I remember trying to solve for zero

Answer 8

then solve for zeros of the bottom:

(3x-1)(2x+5) = 0, for what values of x?

Answer 9

making the equation equal to zero?

Answer 10

yes exactly

Answer 11

recall your multiplication tables .... 0 was one of the simplest ones to remember

Answer 12

given a product of a and b

ab = 0 when a=0, or b=0, or both equal 0

Answer 13

Anything times zero is zero lol

Answer 14

yes :)

so

(3x-1)(2x+5) = 0, when 3x-1 = 0 , or when 2x+5 = 0

Answer 15

4x/((3x-1)(2x+5))
4x = 0
3x -1 = 0
2x + 5 = 0

Answer 16

4x=0 is not a cardinal sin in this case. we are totally allowed to have a zero on top of a fraction

Answer 17

a function is discontinuous where it is undefined, or where it breaks apart

Answer 18

a fraction is undefined when it has a zero underneath:

n/0 is bad

Answer 19

I get that

Answer 20

so we see that this function is undefined when:

3x -1 = 0
or
2x + 5 = 0

so all we have to do is determine for what values of x that happens

Answer 21

So the numerator is allow to have a zero but the denominator is not allowed

Answer 22

correct

Answer 23

So fill in values for x?

Answer 24

of course, or algebra out some values

Answer 25

im not real sure what process youre thinking of there

Answer 26

3x - 1 = 0 , to solve for x, lets start by adding 1 to each side
+ 1 +1
----------
3x + 0 = 1 , since anything +0 is itself (indentity), this simplifies to

3x = 1 , now to get rid of the 3 stuck there, we divide it off, 3/3 = 1
/3 /3
-------
1x = 1/3 , since anything times 1 is itself (identity), this simplifies to

x = 1/3


the same concepts can be applied to the other factor

Answer 27

3x -1 = 0
3x = 0 + 1
or
2x + 5 = 0
2x = 0 + 5

Answer 28

2x = -5 , but yeah

Answer 29

yeah i forgot to flip the sign

Answer 30

if your intent is to "flip the sign" and "move things to the other side"; then you are not applying any sound mathematical principals to this

Answer 31

there are 5 simple properties to algebra, and they can prevent a world of mistakes

Answer 32

1) ab = ba , commutative property

2) (ab)c = a(bc) , associative property

3) \(aa^{-1}=e\), inverse property; the inverse in addition is the negative, the inverse in multiplication is dividing by the reciprocal

4) \(ae=a\), identity property; the identity in addition is +0, the identity in multiplication is *1

5) a(b+c) =ab + ac , distributive property ... multiplication distributes over addition

Answer 33

2x + 5 = 0 , addition inverse, -5
- 5 -5
-----------
2x + 0 = -5 , addition identity

2x = -5 , multiplicative inverse, /2
/2 /2
--------
1x = -5/2 , multiplicative identity

x = -5/2 , multiplicative identity

Answer 34

okay so then we try to get x alone

Answer 35

I understand that

Answer 36

yes, by using the properties of algebra, we can isolate the variable

Answer 37

thanks

Answer 38

signs reverse on the other side of the equation

Answer 39

:) or make up some properties as we go .... the sign reverse on the other side property for example.

head math is great, but it has its drawbacks is all

Answer 40

okay so the inverse becomes the identity

Answer 41

correct, applying the inverse of a given element, produces the identity element

Answer 42

inverse meaning the opposite and identity the after math

Answer 43

yep

Answer 44

so this function is discontinuous at x = -5/2

Answer 45

that is one of the places yes

Answer 46

the other one is at x=1/3

Answer 47

the strategy in determining discontinuity is in finding the parts of the function that can "go bad"

dividing by 0 is bad

taking the even-root of a negative number is bad among the Reals

taking the logarothm of 0 or less is bad

those seem to be the big ones to watch for

Answer 48

Okay thanks you up for another one with lim?

Answer 49

i can take a stab at it .. i only have so much wits about me in a day before I start to go stupid lol

Answer 50

lmao yeah thats how I feel right about now