Question

find the limit of 3x^2+6x-9/2x^2-2 as x approaches 1

Answer 1

You might find this site useful: http://archives.math.utk.edu/visual.calculus/1/limits.7/
It has good walk-through tutorials on this topic.

Answer 2

you basically just need to brush up on factoring

Answer 3

(a+b)^2=a^2+2ab+b^2, if you factor a 3 out of that numerator, you will have this situation

Answer 4

yeah how do i factor 9 to add up to 6

Answer 5

or do i not have to

Answer 6

factor out a 3 first, it will make it much easier

Answer 7

ive got (x+3)(x-3)

Answer 8

thats wrong

Answer 9

thats a difference of 2 squares

Answer 10

so what do i do

Answer 11

if you expanded that you'd get x^2-9

Answer 12

this part 3x^2+6x-9

Answer 13

factor out a 3

Answer 14

3,6,9 all have a common factor of 3 here

Answer 15

3(x^2 +6x-9)

Answer 16

you have to factor the 3 out of the whole numerator so that when you multiply it you get the original expression back

Answer 17

what you just did will yield 3x^2 + 18x -27

Answer 18

3(x^2-2x-3)

Answer 19

+2x

Answer 20

good

Answer 21

now factor the denominator

Answer 22

very much the same thing, guess which number you're pulling out?

Answer 23

2(x^2-1)

Answer 24

yes

Answer 25

now factor (x^2-1)

Answer 26

(difference of 2 squares), i mentioned it a little bit ago

Answer 27

hmm im not sure here

Answer 28

hehe you just did it mistakenly earlier

Answer 29

remember you typed (x-3)(x+3)

Answer 30

oh that

Answer 31

(x+1)(x-1)

Answer 32

yes, now it's all factored. put it all together and cancel like terms

Answer 33

ok but could i have plug in 1 and get an answer

Answer 34

actually, you can further factor the numerator

Answer 35

right now you have the numerator at (x^2+2x-3)

Answer 36

you could not have p lugged 1 into the original equation before factoring it

Answer 37

look at the original denominator

Answer 38

2x^2-2

Answer 39

if you plugged a 1 in here, you'd get a divide by 0 error

Answer 40

i see you will just get 0/0

Answer 41

so try factoring x^2+2x-3

Answer 42

(x-1)(x+3)

Answer 43

good

Answer 44

now everything is factored

Answer 45

so when i cancel i get x+3/x+1

Answer 46

don't forget about the 3 and 2 you factored out

Answer 47

3(x+3)/(2(x+1)

Answer 48

at this point you can plug in 1 and you will not get a divide by 0 error

Answer 49

because you cancelled out the (x-1)

Answer 50

ok i get 12/4

Answer 51

when i reduce i get 3/1

Answer 52

yes. that's it

Answer 53

thanks for the help

Answer 54

3

Answer 55

np

Answer 56

i have another limit problem but its approaching infinity

Answer 57

ok, let's have it

Answer 58

x^2 + 2x-3/2x^2-2 as x approaches infinity, what is the limit

Answer 59

now look at this numerator and denominator

Answer 60

you already factored them in the last problem

Answer 61

give me your factored equation for this problem

Answer 62

(x-1)(x+3)/2(x^2-1)

Answer 63

the denominator further factors out to (x-1)(x+1)

Answer 64

yes, now cancel

Answer 65

x+1/x+1

Answer 66

or 2x+1

Answer 67

what happened to x+3?

Answer 68

my final looks like this (x+3)/(2x+1)

Answer 69

yes

Answer 70

2x+2

Answer 71

no

Answer 72

2(x+1) then you foil

Answer 73

that's as far as you can factor it: (x+3)/[2(x+1)]

Answer 74

you cant do 2x+2?

Answer 75

what's your thinking on that? just trying to see where you're going wrong

Answer 76

oh my mistake, i see what you were doing

Answer 77

thats not a big deal to expand the denominator to 2x+2

Answer 78

so youd have (x+3)/(2x+2)

Answer 79

i thought you meant the whole equation factored out to that

Answer 80

if you have 2(x+1)...why not just foil (2)(x)=2x...2(1)=2...2x+2...

Answer 81

you can, but it's generally not necessary after you've already factored

Answer 82

plus if you do it too early you'll have to factor it again later

Answer 83

oh ok

Answer 84

so since i can't plug in infinity...what should i do

Answer 85

now you have to think what would happen to f(x) is you kept plugging in very large numbers

Answer 86

it would remain large

Answer 87

nope

Answer 88

try plugging in 100 just to test it

Answer 89

well it might cut down...but at the end it would still be large

Answer 90

100+3/2(100+1)=103/202= .50

Answer 91

ok now 1000

Answer 92

the same .50

Answer 93

ok

Answer 94

so 1/2?

Answer 95

1 sec

Answer 96

that's right

Answer 97

ok thanks for the help

Answer 98

sure