Right and left hand limits of (sin x)^tan x at x = 0

[erisedk]

What is the right hand and left hand limit of (sinx)^tanx?
I know this is an indeterminate form 0^0 but what are the RHL and LHL because though I intuitively know that 0^0 is indeterminate, I don't understand what the right hand and left hand limits are?

 

[Maged Saeed]

As I implement!

$$\lim_{x\rightarrow 0}sinx^{tanx}$$

look at the graph of the function

http://www.wolframalpha.com/input/?i=sin x^{tan x}

And this is intuitively reasonable,
Let us assume a very small value approaching to zero for theta [in radians] , say 0.00000001, then the value will be very close to 1
This is the limit from the right .
And the limit from the lift doesn't exist since you x^x is not always valid for negative numbers..,Hope that is right and what you are looking for ,,
:)

 

[HallsofIvy]

It doesn't make sense to talk about "limits" at all without saying what x itself if going to. I presume here you mean "limit as x goes to 0". The "left hand limit" would be as x approaches 0 "from the left" on the number line- that is, x is always negative. The "right hand limit" would be as x approaches 0 "from the right on the number line- x is always positive.

You should be able to see from your graph that if x is approaching 0 "from the right" or "from above", then f(x) goes to 1 while it cannot approach 0 "from the left" or "from below" because, as Maged Saeed said, sin(x)^tan(x) is not defined there.

 

[erisedk]

Ok thanks :D