Question

Using limits to find the slant asymptote for (x-2)^2/(x+3)

Asymptote: y=ax+b

Finding a:
Lim x--> + infinity f(x)/x=a

What is the equation for finding b?

Answer 1

um well u can find the slant asymptote just but using long division, with limits we can expand the numerator first

Answer 2

How would you do this using limits? (sorry, my teacher required us to do this with limits!)

Answer 3

alright lets try this

Answer 4

expand the numerator first

Answer 5

(x^2-4x+4)/(x^2+3x)

Answer 6

now divide the function by x

Answer 7

I mean over x+3!

Answer 8

you are a step ahead of me haha

Answer 9

now divide the numerator and denominator by the highest power (x^2)

Answer 10

so a=1

Answer 11

yep

Answer 12

but what would b =?

Answer 13

because the slant asymptote is y=ax+b
a=1
so y=x+b

Answer 14

to find b you can only use long division...

Answer 15

no limits are involved in finding b, only a

Answer 16

Ok thank you for your help!

Answer 17

hold up!

Answer 18

do division first and tell me what you get

Answer 19

x-7?

Answer 20

now b = lim [Quotient - mx]