Question

find the lim as x approaches 0 of x squared divided by sin squared x

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

oh i see

Answer 7

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?

Answer 8

you could divide top and bottom by x

but I just know my reciprocals :p
example
\[x=\frac{1}{\frac{1}{x}} \text{ or } 5=\frac{1}{\frac{1}{5}}\]

Answer 9

duhhh omg i understand now

Answer 10

thanks @freckles and @IrishBoy123

Answer 11

np