v.s
Find the limit.
lim 3 − 3 tan x/sin x − cos x
x→π/4
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zordoloom
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Could you write out how this looks. the division sign doesn't really indicate where the equation is divided.
zordoloom
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At least put parenthesis where they belong.
v.s
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lim (3 − 3 tan x)/(sin x − cos x)
x→π/4
frx
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First try to just put in the value pi/4 and decide if the function is defined in that point
zordoloom
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you'll get -3sqrt(2)
frx
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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
v.s
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okaaaaaaaaay thambi
v.s
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how do i simplify this?
chrisplusian
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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
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sorry meant numerator
chrisplusian
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and that should have been three times sine over cosine sorry I am messing it up pretty bad
v.s
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loll
itss okayy
v.s
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i dont get the question
Coolsector
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\[\frac{ 3-3\tan(x) }{ \sin(x) - \cos(x) } \times \frac{ \sin(x) +\cos(x) }{ \sin(x) +\cos(x) }\]
Coolsector
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\[\frac{ 3\sin(x) - 3\frac{ \sin^2(x) }{ \cos(x) } + 3\cos(x) -3\sin(x) }{ \sin^2(x) -\cos^2(x) }\]
Coolsector
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\[\frac{ - 3\frac{ \sin^2(x) }{ \cos(x) } + 3\cos(x) }{ \sin^2(x) -\cos^2(x) }\]
Coolsector
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\[\frac{ - 3\sin^2(x) + 3\cos^2(x) }{ \cos(x)[\sin^2(x) -\cos^2(x)] } = \frac{ -3 }{ \cos(x) }\]
v.s
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sorry i was busy
v.s
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so i sub in pi/4
Coolsector
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yes
v.s
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-3/(1/sqroot2)
Coolsector
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which simplifies into -3sqrt(2)
v.s
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-sqroot2/3
Coolsector
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no .. -3 * sqrt(2)
v.s
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yeye
v.s
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i gett it
Coolsector
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\[-3\sqrt2\]
Coolsector
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like this