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AmTran_Bus
 one year ago
Help finding crazy limit!
AmTran_Bus
 one year ago
Help finding crazy limit!

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AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0I need to find the limit as x approaches zero of (e^x 6)/(sin 4x) The problem is the online homework wants the limit as x approaches 0, but don t only the left and right hand limits exist? Check the atached image for the solution choices they provide. I thought it was negative infinity for lim as x approaches 0+ and infinity for x approaches 0.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2You're correct. Looks there is a typographical error, the exponent 4 should be in the exponent i guess http://www.wolframalpha.com/input/?i=lim%28x%5Cto+0%29%5Cfrac%7B%5Cleft%28e%5Ex6%5Cright%29%7D%7B%5Csin%5E4+%5Cleft%28x%5Cright%29%7D

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3hint: we can write this: \[\Large \frac{{{e^x}  6}}{{\sin \left( {4x} \right)}} = \frac{{{e^x}  6}}{{4x}}\frac{1}{{\frac{{\sin \left( {4x} \right)}}{{\left( {4x} \right)}}}}\]

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0Oh ok. Thanks to both of you.

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0Wait, isnt that going to come out as one @Michele_Laino And ganeshie8 said inf?

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0My mistake, I miscalculated @Michele_Laino

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Doing what Michele did helps you get rid of the sin(4x) portion of it. Which just makes it easier to calculate the left and right hand limits to show that it is \(\infty\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2it is infy if you let sin(4x) be sin^4(x) but as the expression stands, the limit is DNE as you said

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0Oh well, I can retake it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oops, didnt recognize ganeshie's wolfram link was for sin^4(x), lol

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3I don't understand: 4 is an exponent or it is a factor?

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0It was like the attachment said.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3it is a factor, as I can see

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3in that case, your limit doesn't exist since we have to consider the graph of the fuinction 1/x, namely: dw:1433615875097:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3I think we have this: \[\large \begin{gathered} \mathop {\lim }\limits_{x \to 0 + } \frac{{{e^x}  6}}{{\sin \left( {4x} \right)}} = \mathop {\lim }\limits_{x \to 0 + } \frac{{{e^x}  6}}{{4x}} \times \mathop {\lim }\limits_{x \to 0 + } \frac{1}{{\frac{{\sin \left( {4x} \right)}}{{\left( {4x} \right)}}}} =  \infty \hfill \\ \hfill \\ \mathop {\lim }\limits_{x \to 0  } \frac{{{e^x}  6}}{{\sin \left( {4x} \right)}} = \mathop {\lim }\limits_{x \to 0  } \frac{{{e^x}  6}}{{4x}} \times \mathop {\lim }\limits_{x \to 0  } \frac{1}{{\frac{{\sin \left( {4x} \right)}}{{\left( {4x} \right)}}}} = + \infty \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, that is what you have. Something wrong with the question. You would think it was meant to be one of the variations ganeshie posted.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.3please substitute x=0.01, into your original expression, what do you get?
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