How do you find the limit as x approaches (pi/2)- of (tanx)^x ?
回答 (3)
2017-05-10 9:43 pm
I graphed that function, and it looks like +infinity to me.
tan( pi/2) is infinite,and infinity to any finite power is infinite,
tan( pi/2) is infinite,and infinity to any finite power is infinite,
2017-05-10 8:58 pm
Let y= (tan x)^x
ln y = x ln (tan x)
= lim x-->pi/2 x * lim x-->pi/2 ln (tan x)
= (pi/2)* ∞
= ∞
ln y -->∞
y --> e^∞ = ∞
ln y = x ln (tan x)
= lim x-->pi/2 x * lim x-->pi/2 ln (tan x)
= (pi/2)* ∞
= ∞
ln y -->∞
y --> e^∞ = ∞
2017-05-10 8:44 pm
Infinity
To see how things are going note that pi/2 ~ 1.57079632679
So, x = 1.57079 is near pi/2
(tanx)^x ~ 15408148753.6
there may well be a better and more formal way to calculate the limit
To see how things are going note that pi/2 ~ 1.57079632679
So, x = 1.57079 is near pi/2
(tanx)^x ~ 15408148753.6
there may well be a better and more formal way to calculate the limit
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