anonymous
  • anonymous
find the lim as x approaches 0 of x squared divided by sin squared x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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IrishBoy123
  • 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
freckles
  • freckles
\[\frac{x^2}{\sin^2(x)}=\frac{x}{\sin(x)} \cdot \frac{x}{\sin(x)} \\ \text{ you should be able to use } \lim_{x \rightarrow 0} \frac{x}{\sin(x)}=1 \]
anonymous
  • anonymous
isnt it lim x approaches o sin x over x =1

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anonymous
  • anonymous
because my professor wants us to use that theorem but i can't figure out how to do it
freckles
  • freckles
the one I mentioned is also true \[\frac{x}{\sin(x)}=\frac{1}{\frac{\sin(x)}{x}} \rightarrow \frac{1}{1} =1 \text{ as } x \rightarrow 0\]
anonymous
  • anonymous
oh i see
anonymous
  • 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?
freckles
  • freckles
you could divide top and bottom by x but I just know my reciprocals :p example \[x=\frac{1}{\frac{1}{x}} \text{ or } 5=\frac{1}{\frac{1}{5}}\]
anonymous
  • anonymous
duhhh omg i understand now
anonymous
  • anonymous
thanks @freckles and @IrishBoy123
freckles
  • freckles
np

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