anonymous one year ago find the lim as x approaches 0 of x squared divided by sin squared x

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1. IrishBoy123

this is a famous limit, just up side down and squared $\lim\limits_{x \to 0}\frac{x^2}{\sin^2 x}$ do you have any ideas? you cannot use L'Hopital for this one. in fact i don't think you can use calculus at all for this one. sticking my neck out there but makes sense to me! @freckles @Empty @ganeshie8

2. freckles

$\frac{x^2}{\sin^2(x)}=\frac{x}{\sin(x)} \cdot \frac{x}{\sin(x)} \\ \text{ you should be able to use } \lim_{x \rightarrow 0} \frac{x}{\sin(x)}=1$

3. anonymous

isnt it lim x approaches o sin x over x =1

4. anonymous

because my professor wants us to use that theorem but i can't figure out how to do it

5. freckles

the one I mentioned is also true $\frac{x}{\sin(x)}=\frac{1}{\frac{\sin(x)}{x}} \rightarrow \frac{1}{1} =1 \text{ as } x \rightarrow 0$

6. anonymous

oh i see

7. anonymous

for this equation that you just gave me, in order to get the 1 over the sinx divided by x did you divide by 1?

8. freckles

you could divide top and bottom by x but I just know my reciprocals :p example $x=\frac{1}{\frac{1}{x}} \text{ or } 5=\frac{1}{\frac{1}{5}}$

9. anonymous

duhhh omg i understand now

10. anonymous

thanks @freckles and @IrishBoy123

11. freckles

np