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clara1223
 one year ago
find the limit as x approaches 0 of (sin^2)(4x)/3x
clara1223
 one year ago
find the limit as x approaches 0 of (sin^2)(4x)/3x

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you know L'Hopital's Rule?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5Hint: \[\Large \lim_{x \to 0}\left(\frac{\sin(x)}{x}\right) = 1\]

clara1223
 one year ago
Best ResponseYou've already chosen the best response.1I'm just not sure how to simplify it to make it look like that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ahh yes squeeze theorem good one @jim_thompson5910

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[\sin^2(u)=\sin(u) \cdot \sin(u)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I've gotten so used to L'Hopital's rule I'm lazy

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5I suggest first breaking up the square as freckles wrote \[\Large \frac{\sin^2(4x)}{3x}=\frac{\sin(4x)}{3}*\frac{\sin(4x)}{x}\] then try to make the denominator x turn into 4x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Btw once you have completed the problem using jim's method I would suggest you check this out: https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule as you will eventually use it. It makes problems like this just a simple matter of taking derivatives. Though if you haven't seen it in class I would recommend against using it in the solution for this problem in particular, although if you fell able you should try it out and compare the effort it takes using both methods :D

clara1223
 one year ago
Best ResponseYou've already chosen the best response.1@jim_thompson5910 so I am able to get to \[\frac{ 4 }{ 3 }\lim_{x \rightarrow 0}\frac{ \sin x }{ 1 } \times \frac{ \sin x }{ x }\] but how do I get an x into the first denominator?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5there's no need because you can simply plug in x = 0 for that first fraction

clara1223
 one year ago
Best ResponseYou've already chosen the best response.1so then would the answer be \[\frac{ 4 }{ 3 }\times0\times1\]

clara1223
 one year ago
Best ResponseYou've already chosen the best response.1Great! so the answer is 0. thanks!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5you're welcome
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