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amyna
 one year ago
find the limit
amyna
 one year ago
find the limit

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amyna
 one year ago
Best ResponseYou've already chosen the best response.0how do i do the l'hopitals rule for this problem?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I guess you are asking how to differentiate sin(pi*x) since I'm certain you know how to differentiate x

amyna
 one year ago
Best ResponseYou've already chosen the best response.0so far i got: 1+cos pi x / 1cos pi x ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{d}{dx}(\sin(\pi x)) =(\pi x)' \cos(\pi x) \text{ by chain rule }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2well (pi*x)'=pi not 1

freckles
 one year ago
Best ResponseYou've already chosen the best response.2anyways you should be able to use direct sub after the first round of l'hospital once you differentiate sin(pi*x) correctly

amyna
 one year ago
Best ResponseYou've already chosen the best response.0so pi x + cos pi x / pi x  cos pi x ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2derivative of just x is 1... why do you put pi x? you still aren't writting the derivative of sin(pi*x) is pi*cos(pi*x)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{d}{dx}(x)=1 \\ \frac{d}{dx} \sin( \pi x)=(\pi x)' \cos(\pi x)= \pi \cos(\pi x)\]

amyna
 one year ago
Best ResponseYou've already chosen the best response.0oh okay so the answer is 1+ pi / 1 pi

freckles
 one year ago
Best ResponseYou've already chosen the best response.2yes that is right \[\lim_{x \rightarrow 0} \frac{x+ \sin( \pi x)}{x \sin (\pi x)} \\ \lim_{x \rightarrow 0} \frac{\frac{d}{dx}(x + \sin(\pi x))}{\frac{d}{dx}(x \sin(\pi x))} \\ \lim_{x \rightarrow 0} \frac{\frac{d}{dx}(x)+\frac{d}{dx}\sin(\pi x)}{\frac{d}{dx}(x)\frac{d}{dx}\sin (\pi x)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2well almost it should be (1+pi)/(1pi)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.11+2sin(px)/x  xsin(px)  x + sin(px) (x sin(px))  2sin(px) (2sin(px) 2sin^2(px)/x)  2sin^2(px)/x sin(px) = 0 when x=0, so i spose we could view this as 1+2sin(px)/x as x to 0, maybe?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1i think my thought has an error tho

freckles
 one year ago
Best ResponseYou've already chosen the best response.2are you doing yours with l'hospital ? I was trying to follow all those broken line thingys...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1i was trying to do long division :) to see what a series might be represented as

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\lim_{x \rightarrow 0} \frac{x + \sin( \pi x)}{x \sin( \pi x)} \\ \text{ divide top and bottom by } \pi x \\ \lim_{x \rightarrow 0} \frac{\frac{x}{\pi x}+\frac{\sin(\pi x)}{\pi x}}{\frac{x}{\pi x}\frac{\sin(\pi x)}{\pi x}} \\ =\frac{\frac{1}{\pi}+1}{\frac{1}{\pi}1} \\ \text{ now multiply top and bottom by } \pi \\ =\frac{1+\pi}{1\pi}\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1squashing my creativity are you .... ;)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2lol no let's try the long division thingy

freckles
 one year ago
Best ResponseYou've already chosen the best response.2or let me look at yours since I know what I'm looking at :p

amyna
 one year ago
Best ResponseYou've already chosen the best response.0lol Thanks for you help guys! :)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1maybe fliiping the order of the terms might help .. one way is x to infinity, the other is x to zero ... ive noticed this but i cant see why.

freckles
 one year ago
Best ResponseYou've already chosen the best response.2your division seems great

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so you get this : \[\lim_{x \rightarrow 0} (1+2 \frac{\sin(\pi x)}{x}+2 \cdot \frac{\sin^2( \pi x)}{x(x \sin( \pi x)})\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1i was thinking we could factor our a sin(px) to zero out all but the first 2 terms .. but that seems to be where my idea goes awry.

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\lim_{x \rightarrow 0} (1+2 \frac{\sin(\pi x)}{x}+2 \cdot \frac{\sin^2( \pi x)}{x(x \sin( \pi x))})\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1i think i broke the wolf :/

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[1+2 \pi +2 \cdot \lim_{x \rightarrow 0} \frac{\sin^2(\pi x)}{x^2 x \sin(\pi x)} \\ \\ \text{ for the last quotient there divide top and bottom by } x^2 \\ 1+2 \pi +2 \cdot \frac{\pi^2}{1\pi} \] I still go back to my old ways using that one famous limit thingy

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I think I did something wrong though

freckles
 one year ago
Best ResponseYou've already chosen the best response.2oh no it was the same as previous answer
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