Question

lim of infinity sqrt9x to the 6th power -x all over xsquared +1 I got 3 to be the limit. If thats right, im not sure how I got the answer

Answer 1

\[\lim_{x\rightarrow \infty}\frac{\sqrt{9x^6-1}}{x^2+1}\]

Answer 2

if so, should be infinity

Answer 3

no I think the -1 is outside the square root

Answer 4

\[\lim_{x\rightarrow \infty}\frac{\sqrt{9x^6-x}}{x^2+1}\]

Answer 5

then it simplifies to (3x^3 - 1)/(x^2 + 1)

Answer 6

Then divide top and bottom by x^3 and you are left with 3/1

Answer 7

oh no!

Answer 8

numerator is a cube, denominator is a square
plus how does is simplify?

Answer 9

nay is right

Answer 10

aahh yeas you're right

Answer 11

again you do this with your eyeballs. ignore everything but highest power. the numerator is not a polynomial, but
\[\sqrt{x^6}=x^3\] so think "degree 3"
denominator is a polynomial of degree 2
bigger numerator means bigger number, so no limit (or it is infinity)

Answer 12

its square root of 9x to the 6th power - x all over x cubed plus 1

Answer 13

ooooooooooooooooooh x cubed!!!!

Answer 14

hmmmm not to give you a hard time... but you wrote squared!

Answer 15

then you are right
good work

Answer 16

haha yeah I think I solved it with x^3...yeah good job calculus.

Answer 17

good work to nayeaddo too

Answer 18

so then a problem like x+x cubed+x to the 5th power all over 1-x squared +x to the fourth power would be infinity???

Answer 19

lol @ satellite73

Answer 20

can you maybe write it using the equation tool?

Answer 21

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

Answer 22

that is infinity because the degree of the numerator is higher than the denominator

Answer 23

think about what it would be like if x were 1,000,000 = 10^6

Answer 24

\[(x + x^3 + x^5)\]/ (1 - x^2 + x^4)

Answer 25

but solutions is the same regardless.

Answer 26

or even ten for that matter. suppose you made x = 10
you would have
\[\frac{101010}{10101}\]

Answer 27

numerator is bigger than denominator by a factor of ten. this gets huge as x gets huge