okay so I am trying to find the limit. LIM sin (squared) 3x / x (squared) x--> 0 I am soo unsure of how to do this. Any suggestions?? btw we havent gone over the L'H rule yet...
Follow Math Help Forum on Facebook and Google+
Originally Posted by MZTakara okay so I am trying to find the limit. LIM sin (squared) 3x / x (squared) x--> 0 I am soo unsure of how to do this. Any suggestions?? btw we havent gone over the L'H rule yet... $\displaystyle \displaystyle\lim_{x\to 0}\frac{\sin^2(3x)}{x^2}=\lim_{x\to 0}\frac{9(\sin^2(3x))}{(3x)^2}=9\cdot\lim_{x\to 0}\left(\frac{(\sin(3x))}{(3x)}\right)^2=\cdots$
For small values of x, $\displaystyle \sin x \approx x $.
Use this guy $\displaystyle \displaystyle \lim_{x\to 0} \frac{\sin x }{x} = 1$ Make $\displaystyle \displaystyle \frac{\sin^2 3x }{x} = \frac{\sin 3x }{x}\times \frac{3}{3}\times \frac{\sin 3x }{1} $
but sin is squared....that does not matter???
Originally Posted by dwsmith $\displaystyle \displaystyle\lim_{x\to 0}\frac{\sin^2(3x)}{x^2}=\lim_{x\to 0}\frac{9(\sin^2(3x))}{(3x)^2}=9\cdot\lim_{x\to 0}\left(\frac{(\sin(3x))}{(3x)}\right)^2=\cdots$ $\displaystyle \displaystyle9\cdot\lim_{x\to 0}\left(\frac{(\sin(3x))}{(3x)}\right)^2=\cdots$ Let 3x = t $\displaystyle \displaystyle\lim_{t\to 0}\left(\frac{(\sin(t))}{(t)}\right)^2=\cdots$ What is 1 squared?
one....>_> Thanks
Originally Posted by MZTakara but sin is squared....that does not matter??? No. $\displaystyle \sin^{2}(3x) = \sin(3x)* \sin(3x) \approx 3x*3x = 9x^{2} $ for small values of x.
lol..ima so fail this semester.
Originally Posted by MZTakara lol..ima so fail this semester. Not when you've got MHF to turn to when you're feeling low :P
View Tag Cloud