+129852 I think the question is asking to evaluate the tan inverse as it approaches negative and positive infinity. And the questioner wants to know if this can be done without graphing.
And we want to know this:
lim tan-1(x) as x→±∞
Let y= tan-1(x)
Then tan(y) = x
And as x → +∞, then y→ pi/2
Similarly, as x → -∞, then y → -pi/2
So, lim tan-1(x) as x→+∞ = pi/2 and lim tan-1(x) as x→-∞ = -pi/2
+118677 Sorry 315, besides the fact that it is late and my brain is shutting down. My poor eyes really cannot read that. LOL
+1832 No problem my instractor Help me when you are ready ..
And I hope that I don't find this question in my quiz tomorrow =D
+129852 I think the question is asking to evaluate the tan inverse as it approaches negative and positive infinity. And the questioner wants to know if this can be done without graphing.
And we want to know this:
lim tan-1(x) as x→±∞
Let y= tan-1(x)
Then tan(y) = x
And as x → +∞, then y→ pi/2
Similarly, as x → -∞, then y → -pi/2
So, lim tan-1(x) as x→+∞ = pi/2 and lim tan-1(x) as x→-∞ = -pi/2
+1832 ok thats well !
but you wrote that (( And as x → +∞, then y→ pi/2 ))
and I think it should be , when x → pi/2 , then y → +∞
right ?
+129852 Notice what I was evaluating when I wrote that.......it was...... tan(y) = x
And as x approaches infinity, y approaches pi/2.
If x just approaches pi/2, then y just approaches about 1. (in radians).
Graph the tangent inverse function......you will see that as x approaches infinity, y approaches pi/2 ... and as x approaches negative infinity, y approaches -pi/2.
