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Can anyone help with this question? Im not sure what method to use...

Find the limit of ((x^2)+sinx)/(x^2)

as x approaches infinity. Thanks

Find the limit of ((x^2)+sinx)/(x^2)

as x approaches infinity. Thanks

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#2

If you split the fraction up into (x^2)/(x^2)+(sinx)/(x^2), then thi should make the question easier

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#3

use with the Pinching theorem - adding 1 to the inequality - the answer is pretty obvious

(EDIT): previous poster`s post is easier, though!

(EDIT): previous poster`s post is easier, though!

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(Original post by

If you split the fraction up into (x^2)/(x^2)+(sinx)/(x^2), then thi should make the question easier

**ccfcadam36**)If you split the fraction up into (x^2)/(x^2)+(sinx)/(x^2), then thi should make the question easier

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#5

with thr Pinching theorem (as above) you can show that - because you take the modulus of Sin(x) (since it doesn`t deviate outside +/-1):

so you get, adding the "1":

so you get, adding the "1":

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#6

(Original post by

Okay, so im trying to find limit of 1+(sinx)/(x^2), I know sinx will be between -1 and 1, and x^2 will go to infinity, so can i just say that (sinx)/(x^2) tends to 0, so the limit is 1? And is there a special rule for finding (sinx)/(x^2)?

**Vividness**)Okay, so im trying to find limit of 1+(sinx)/(x^2), I know sinx will be between -1 and 1, and x^2 will go to infinity, so can i just say that (sinx)/(x^2) tends to 0, so the limit is 1? And is there a special rule for finding (sinx)/(x^2)?

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Thanks for your help on that one, just one more I'm stuck on:

limit of (sqrt(9x+1))/(x+1) as x approaches infinity, any ideas?

limit of (sqrt(9x+1))/(x+1) as x approaches infinity, any ideas?

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#8

(Original post by

Thanks for your help on that one, just one more I'm stuck on:

limit of (sqrt(9x+1))/(x+1) as x approaches infinity, any ideas?

**Vividness**)Thanks for your help on that one, just one more I'm stuck on:

limit of (sqrt(9x+1))/(x+1) as x approaches infinity, any ideas?

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(Original post by

Firstly,Consider the limit of (9x+1)/(x+1) by dividing everything by x to give (9+1/x)/(1+1/x), then if you know the limit of 1/x as x tend to infinity then you can work out the limit of the whole thing

**ccfcadam36**)Firstly,Consider the limit of (9x+1)/(x+1) by dividing everything by x to give (9+1/x)/(1+1/x), then if you know the limit of 1/x as x tend to infinity then you can work out the limit of the whole thing

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#10

(Original post by

So without the square root the limit would be 9, but how can i adapt this solution to find the limit when the numerator is square rooted?

**Vividness**)So without the square root the limit would be 9, but how can i adapt this solution to find the limit when the numerator is square rooted?

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(Original post by

with thr Pinching theorem (as above) you can show that - because you take the modulus of Sin(x) (since it doesn`t deviate outside +/-1):

so you get, adding the "1":

**Hasufel**)with thr Pinching theorem (as above) you can show that - because you take the modulus of Sin(x) (since it doesn`t deviate outside +/-1):

so you get, adding the "1":

limit of (sqrt(9x+1))/(x+1) as x approaches infinity

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#12

**Vividness**)

So without the square root the limit would be 9, but how can i adapt this solution to find the limit when the numerator is square rooted?

You can still divide top and bottom by x but note that you have to take factor 1/x^2 inside the square root.

Alternatively, you can make some "brute force" approximations - x+1 > x so 1/(x+1) < 1/x gives you a simpler thing to work with, and then use the squeeze theorem to put the limit between 2 bounds.

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#13

(Original post by

Thanks for that, any ideas on this one?

limit of (sqrt(9x+1))/(x+1) as x approaches infinity

**Vividness**)Thanks for that, any ideas on this one?

limit of (sqrt(9x+1))/(x+1) as x approaches infinity

This gets rid of the root on the numerator - moving it to the denominator where it`s easier to eliminate.

we then end up with:

splitting up the first part, we get:

Now take limits ( )

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#14

**Vividness**)

Thanks for your help on that one, just one more I'm stuck on:

limit of (sqrt(9x+1))/(x+1) as x approaches infinity, any ideas?

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