Question

What are the vertical and horizontal asymptotes of y=1+(1/x)+(1/x^2)?

Answer 1

do you know what happens at vertical asymptotes?

Answer 2

what do you think will be the value of y at a vertical asymptote?

Answer 3

vertical asymptote is x=-1

Answer 4

I dont know. thats why im asking. I tried doing the limit as x approaches infinity and i got a horizontal asymptote of 1

Answer 5

your horizontal asymptote is correct :)

Answer 6

now think about what happens at a vertical asymptote - try drawing a picture and see if you can work it out

Answer 7

How do you get a vertical asymptote of -1?
and the whole point of finding the asymptotes is so that i can draw the graph

Answer 8

that is wrong - please ignore it

Answer 9

but do you understand what a vertical asymptote represents?

Answer 10

am right

Answer 11

horizontal asymptote is limit of y as x approaches infinity
so vertical asymptote is ...

Answer 12

try to do thn u ll knw

Answer 13

another way to look at it is as follows:
x tends to plus or minus infinity as the curve approaches a horizontal asymptote

Answer 14

now think about what a vertical asymptote could mean

Answer 15

you can only find it if you know what it represents - i.e. you need to understand what a vertical asymptote is before you can calculate it for this curve.

Answer 16

horizontal is 1

Answer 17

hint: think about what happens as x becomes smaller and smaller

Answer 18

what happens to y?

Answer 19

0=1+(1/x) thn 1/x=-1 then multiply by x ll be -x=1 then divd by -1 both ll be x=-1

Answer 20

@semaameya I can only help you if you respond to the questions.

Answer 21

so when x becomes smaller, does y approach 1?

Answer 22

look at the terms in your equation - they involve terms like:\[\frac{1}{x}\]what happens to the value of 1/x as x becomes smaller and smaller - approaching zero

Answer 23

Yeah. so when x is approaching 0, 1/x will be 1/0 which is undefined. same thing goes to the 1/x^2. so all we have left will be the first term, which is 1

Answer 24

no - think about this - what is:

1/0.0001 = ?

Answer 25

a really big number.

Answer 26

so now what happens with this:

1/0.00000000001 = ?

is this even larger?

Answer 27

Yeah. so y approaches positive infinity?

Answer 28

perfect!

Answer 29

so as x tends to zero, y tends to positive infinity

Answer 30

so the vertical asymptote is at x=?

Answer 31

if y approaches positive infinity, does this mean there is no vertical asymptote?

Answer 32

no - it means that there is a vertical asymptote there

Answer 33

at x=0?

Answer 34

just like when x tended to infinity, y tended to 1 meant there is a horizontal asymptote at y=1

Answer 35

correct - well done! :)

Answer 36

Thank you so much!.

Answer 37

yw :)