Question

sole this limit :

Answer 1

\[\lim_{x \rightarrow -2} \frac{ x^3+2x^2-4x-8 }{ x+2 }\]

Answer 2

direct subst. 0/0

Answer 3

factor the numerator

Answer 4

(x+2)(x^2+4x+4)

Answer 5

nopes

Answer 6

ohh then i don't know :S

Answer 7

take x^2 common from 1st 2 terms

Answer 8

ohh, are we grouping like the last question ?

Answer 9

yes !

Answer 10

so ?

Answer 11

would the final answer equal zero ?

Answer 12

yup.
did u understand how ?

Answer 13

yupp, same as last one
thanks again :)

Answer 14

welcome ^_^

Answer 15

but i have a question: what would happen if the trinomial didn't group what would i do ?

Answer 16

remember this :
IF YOU GET 0 AFTER DIRECT SUBSTITUTION, THEN YOU MUST BE ABLE TO FACTOR IT OUT.

Answer 17

\[\lim_{x \rightarrow 2} \frac{ 2x^3-5x^2+3x-2 }{ 2x-4 }\]

Answer 18

if for lim x->a
you get a polynomial in numerator =0 when directly substituted, implies x-a MUST be factor of that polynomial

Answer 19

^ i get 0/0 but in order to factor out is it okay if i need to use \[p \in { ... }\]

Answer 20

p ?

Answer 21

values of the last variable

Answer 22

sorry, still i can't understand what p is ?
for the above problem, what is p ?

Answer 23

it would be all the factors of 2

Answer 24

that when substituted would make it zero

Answer 25

x-2 must be factor of 2x^3-5x^2+3x-2
because u get 0 after u put x=2

Answer 26

ohh okay

Answer 27

then do i use synthetic division ?

Answer 28

yup.

Answer 29

u get a quadratic, where u directly put x=2

Answer 30

\[\lim_{x \rightarrow 2}\frac{ (2x^2-x-1)(x-2) }{ 2x-2 }\]

Answer 31

@hartnn

Answer 32

did u miss out 2 or 4 ?

Answer 33

yeah the denominator is 2x-4

Answer 34

i think there is an error in synthetic division, check it

Answer 35

\[\lim_{x \rightarrow 2}\frac{ 2x^2-x+1)(x-2) }{ 2x-4 }\]

Answer 36

yup, now u can cancel x-2 from numerator and denominator

Answer 37

\[\frac{ 2x^2-x+1 }{ x+2 }\]

Answer 38

what ?
how u got x+2 in denominator ?

Answer 39

(x-2)

Answer 40

but x-2 cancels out

Answer 41

yeah then im left with x+2

Answer 42

how x+2 ?

Answer 43

(x-2)/2x-4 is x-2 i think :S

Answer 44

2x-4 = 2 (x-4)
(x-2)/2 (x-2) = 1/ 2

Answer 45

ohhhh :$haha woops

Answer 46

put x=2 in 2x^2-x+1 / 2