Need help with Limits
I don't need any help with actually solving anything, but I need something clarified...
In lim (x ->pi/2) cos(x)/cot(x) why can't I use direct substitution to find the limit?
My teacher told me that I can use direct substitution for polynomial, rational, trig, and log/exp functions when direct substitution doesn't yield undefined values since those functions are continuous on those intervals.
Yet, if I directly input cos(pi/2) / cot(pi/2)
> (0/1) / (0/1) = 0, which is incorrect. Why is this? Neither cosine pi/2 or cotangent of pi/2 are undefined.
May 12, 2012
5 Comments • Newest first
[quote=MachFire]Chances are is that he's in a normal precalculus class, and won't know a thing about derivatives. Like it has been said, just simplify the trig function.....[/quote]
Agreed with this. Any student asking a question like that of the TS, at this time of year, is likely not to be in calculus
[quote=JonBaz]Use L'Hospital's Rule where you take the derivative of the top and the bottom so you get -sin(x)/-(csc(x))^2 which is sin(x)/(csc(x))^2
If you plug in pi/2 then you get sin(pi/2)/(csc(pi/2))^2 = 1 <------ answer
Also, just an FYI, 0/0 is not 0, is it indeterminate and that means you have to simplify the problem to where you don't have 0/0 any more.[/quote]
lol, if you do this question her way, then you pretty much wasted time off your life you'll never get back, when you can easily solve this limit in no less than 3 seconds..
[quote=JonBaz]Use L'Hospital's Rule where you take the derivative of the top and the bottom so you get -sin(x)/-(csc(x))^2 which is sin(x)/(csc(x))^2
If you plug in pi/2 then you get sin(pi/2)/(csc(pi/2))^2 = 1 <------ answer
Also, just an FYI, 0/0 is not 0, is it indeterminate and that means you have to simplify the problem to where you don't have 0/0 any more.[/quote]
Chances are is that he's in a normal precalculus class, and won't know a thing about derivatives. Like it has been said, just simplify the trig function.....
WOW damnit lol I'm such an idiot.
Thank you!
You're completely right OP.
You can use direct substitution for values that don't give undefined results in functions.
Now tell me, what is anything divided by 0?