haleycleoj
haleycleoj
28-03-2017
Mathematics
contestada
lim ln(tan x) as tends to pi/2 from the left
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LammettHash
LammettHash
28-03-2017
Let [tex]x=\arctan y[/tex]. Then [tex]\tan x=y[/tex], and so as [tex]x\to\dfrac\pi2^-[/tex], you have [tex]y\to+\infty[/tex]. The limit is then equivalent to
[tex]\displaystyle\lim_{x\to\frac\pi2^-}\ln(\tan x)=\lim_{y\to\infty}\ln y=\infty[/tex]
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