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## Homework Statement

lim (x-->infinity) [(sqrt(cosX)-cosX)/(x^2)]

## Homework Equations

hey guys, can anyone please help me solve this limit (without a calculator..)

10x!

- Thread starter alexd
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- #1

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lim (x-->infinity) [(sqrt(cosX)-cosX)/(x^2)]

hey guys, can anyone please help me solve this limit (without a calculator..)

10x!

- #2

tiny-tim

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Hi alexd! Welcome to PF!

(have a square-root: √ and an infinity: ∞ )

Hint: draw the graph …lim (x-->infinity) [(sqrt(cosX)-cosX)/(x^2)]

what does it look like?

(erm … you don't mean lim

- #3

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I drew the graph, it seems to be going to zero when x->∞

and unfortunetally it is x->∞ and not x->0

but i'm a bit stuck with the limit...

any ideas on how to approach it (analytically)?

- #4

tiny-tim

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ok … soI drew the graph, it seems to be going to zero when x->∞

how big is the bottom getting? and how big the top?

- #5

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so it's actually not defined when x->∞

The case for x->0 is much easier - the answer is 1/4...

is that what u meant?

- #6

tiny-tim

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YesThe case for x->0 is much easier - the answer is 1/4...

is that what u meant?

Yes itok.. I think I see where u're going with this...

so it's actually not defined when x->∞

just answer my previous question: how do the top and bottom (separately) behave?

- #7

- #8

tiny-tim

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(i can't see your graph yet, but i assume it's upsy-downsy )

Yup!well...

the bottom obviously goes to ∞ when x->∞

I think you're worrying too much about the fact that it obviously doesn't convergeand as for the top.. I have no idea...

that's where i got stuck the 1st time..

what do you do with cosx when x->∞?

but the important point is that it

|cosx| can't be greater than 1 …

so the top/bottom … ?

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