anonymous
  • anonymous
Find the limit. lim 3 − 3 tan x/sin x − cos x x→π/4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Could you write out how this looks. the division sign doesn't really indicate where the equation is divided.
anonymous
  • anonymous
At least put parenthesis where they belong.
anonymous
  • anonymous
lim (3 − 3 tan x)/(sin x − cos x) x→π/4

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More answers

anonymous
  • anonymous
First try to just put in the value pi/4 and decide if the function is defined in that point
anonymous
  • anonymous
you'll get -3sqrt(2)
anonymous
  • anonymous
You see that sin pi/4- cos pi/4 equals zero so the function is undefined at pi/4 so what you want to do is to simplify the function
anonymous
  • anonymous
okaaaaaaaaay thambi
anonymous
  • anonymous
how do i simplify this?
chrisplusian
  • chrisplusian
you can turn your denominator into\[(3-3(\frac{ cosx }{ sinx })\] then split the numerator into two different fractions\[\frac{ 3 }{ sinx-cosx } - \frac{ \frac{ sinx }{ cosx } }{ sinx-cosx }\]
chrisplusian
  • chrisplusian
sorry meant numerator
chrisplusian
  • chrisplusian
and that should have been three times sine over cosine sorry I am messing it up pretty bad
anonymous
  • anonymous
loll itss okayy
anonymous
  • anonymous
i dont get the question
anonymous
  • anonymous
\[\frac{ 3-3\tan(x) }{ \sin(x) - \cos(x) } \times \frac{ \sin(x) +\cos(x) }{ \sin(x) +\cos(x) }\]
anonymous
  • anonymous
\[\frac{ 3\sin(x) - 3\frac{ \sin^2(x) }{ \cos(x) } + 3\cos(x) -3\sin(x) }{ \sin^2(x) -\cos^2(x) }\]
anonymous
  • anonymous
\[\frac{ - 3\frac{ \sin^2(x) }{ \cos(x) } + 3\cos(x) }{ \sin^2(x) -\cos^2(x) }\]
anonymous
  • anonymous
\[\frac{ - 3\sin^2(x) + 3\cos^2(x) }{ \cos(x)[\sin^2(x) -\cos^2(x)] } = \frac{ -3 }{ \cos(x) }\]
anonymous
  • anonymous
sorry i was busy
anonymous
  • anonymous
so i sub in pi/4
anonymous
  • anonymous
yes
anonymous
  • anonymous
-3/(1/sqroot2)
anonymous
  • anonymous
which simplifies into -3sqrt(2)
anonymous
  • anonymous
-sqroot2/3
anonymous
  • anonymous
no .. -3 * sqrt(2)
anonymous
  • anonymous
yeye
anonymous
  • anonymous
i gett it
anonymous
  • anonymous
\[-3\sqrt2\]
anonymous
  • anonymous
like this

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