Question

Evaluate the limit

Lim ((2−x)(3+10x))/((3−3x)(4+4x))
x->INF

Answer 1

Lim = 5/6

Answer 2

can u explain how ?

Answer 3

yup, give me a sec

Answer 4

(2-x)(3+10x)=something -10x2
(3-3x)(4+4x)=something -12x2
In the limit you don't really care about the 'something' since it will grow slower than x2
So Lim = Lim -10x2/-12x2 = -10/-12=5/6

Answer 5

Or if you really want the whole thing,
Lim = Lim (-10x2+17x+6)/(-12x2+12) = Lim -10x2/-12x2 = -10/-12=5/6

Answer 6

Cheers ;)

Answer 7

to clarify:
Syderic distributed, then divided top an bottom by x^2
ax x -> infty only the constants will remain

Answer 8

Syderitic, excuse me :P

Answer 9

*as x-> infty

Answer 10

no prob ;)

Answer 11

Thank u all

Answer 12

one thing about Lim (-10x2+17x+6)/(-12x2+12)
how did you solve it?

Answer 13

hum... well u see: when calculating Lim of p1(x)/p2(x) with p1 and p2 being polynomials
you want to see wich values will be the most 'influents' on limit.

ex (see image)
as can see x3 will be far greater than x2 or x in inf

soo we only look at the terms with greater order and ignore the others, since in inf they will be too small when comparing to those of higher order.

Answer 14

so i ignore (17x+6) and (12) ?