- #1

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[tex] \lim_{x \rightarrow 0} \frac {tanx}{4x} [/tex]

[tex]= \frac {sinx}{cos4x} ? [/tex]

Not really too sure if I manipulated the equation right. Any hints for the next step? Thanks.

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- Thread starter erik05
- Start date

- #1

- 50

- 0

[tex] \lim_{x \rightarrow 0} \frac {tanx}{4x} [/tex]

[tex]= \frac {sinx}{cos4x} ? [/tex]

Not really too sure if I manipulated the equation right. Any hints for the next step? Thanks.

- #2

- 25

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Use l'hopitals rule.

[tex] \lim_{x \rightarrow 0} \frac {tanx}{4x} =\lim_{x \rightarrow 0} \frac {secxtanx}{4}[/tex]

- #3

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Sorry, I haven't learned l'hopitals rule yet and we're not suppose to use it for these questions.

- #4

- 609

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expand tanx in taylor series, and do what you should do...

- #5

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This is going to sound really pathetic but no, we haven't the taylor series either.

- #6

- 609

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[tex] \lim_{x \rightarrow 0} \frac {sinx}{x} =1[/tex]

if yes, you should start from here

- #7

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I think Taylor series is taught way after l'Hôpital's rule,don't u think so?

Daniel.

Daniel.

- #8

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vincentchan said:

[tex] \lim_{x \rightarrow 0} \frac {sinx}{x} =1[/tex]

if yes, you should start from here

That I do know.

- #9

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What about "tangent's" definition...?And the limit of cosine as its argument goes to 0 ?

Daniel.

Daniel.

- #10

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erik05 said:

[tex] \lim_{x \rightarrow 0} \frac {tanx}{4x} [/tex]

[tex]= \frac {sinx}{cos4x} ? [/tex]

Not really too sure if I manipulated the equation right. Any hints for the next step? Thanks.

= 1/4*(sin[x]/x)*(sec[x])

- #11

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Ah...I got it. Thanks all.

- #12

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Solution:

[tex] \boxed{\lim_{x \rightarrow 0} \frac {\tan x}{4x} = \frac{1}{4}}[/tex]

Last edited:

- #13

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How fancy that \boxed{...},too bad u don't know "\tan"...

Daniel.

P.S.BTW,I've searched Mathworld and A & S,couln't find this [itex] tanx [/itex] function...

P.P.S.Neither [itex] sinx[/itex],nor [itex] secxtanx [/itex],but i found [itex] \mbox{sinc}\ x [/itex]...

P.P.P.S.You edited...

Daniel.

P.S.BTW,I've searched Mathworld and A & S,couln't find this [itex] tanx [/itex] function...

P.P.S.Neither [itex] sinx[/itex],nor [itex] secxtanx [/itex],but i found [itex] \mbox{sinc}\ x [/itex]...

P.P.P.S.You edited...

Last edited:

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