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amonoconnor
 one year ago
I'm stuck on this one... I just don't see how to manipulate or substitute to evaluate it without getting 0.
Find the Limit of:
*mathematical expression in first comment"
Thank you! Any and all help is greatly appreciated!
amonoconnor
 one year ago
I'm stuck on this one... I just don't see how to manipulate or substitute to evaluate it without getting 0. Find the Limit of: *mathematical expression in first comment" Thank you! Any and all help is greatly appreciated!

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amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow \pi/4}\frac{ 1 \tan x }{\sin x  \cos x}\]

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0Sorry about the goofy fraction there, I retyped it twice, and the error didn't go away.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \frac{1\color{orangered}{\tan x}}{\sin x\cos x}=\frac{1\color{orangered}{\frac{\sin x}{\cos x}}}{\sin x\cos x}\]Let's multiply top and bottom by cos(x) to get rid of that fraction up there.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm =\frac{\cos x\cos x\frac{\sin x}{\cos x}}{(\sin x\cos x)\cos x}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm =\frac{\cos x\sin x}{(\sin x\cos x)\cos x}\]Can you see where this is heading? :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I dont, Jesus. But good luck!!! <3 xD

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0I understand everything up to here, but.. uhh, where do I go now? :/

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Hmmm, let's factor a 1 out of each term in the numerator. It might click in your brain when we do :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm =\frac{(\sin x\cos x)}{(\sin x\cos x)\cos x}\]

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0.... and the 1 just goes in front of the "lim" part?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ya, it can go where ever you want it to go :)

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0Why don't we switch the signs in the denominator as well?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1You mean when we factored out the 1? Or you're suggesting we should follow that up with another factoring of 1 in the bottom? I'm just a lil confused by the question >.<

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0Yes, like, when you said we factor a 1 out of the top... why aren't we just taking it out of the whole fraction/problem, switching signs in the bottom to make it cosx(cosx  sinx)? Is it because 1 is technically = 1/+1?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Yes, good observation. If we did it to the whole thing, it would be more like 1/1 being taken out, which is really no change at all.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1I'm gonna color something and hopefully it jumps out at you as to why we took a 1 out of the numerator,\[\large\rm =\frac{(\color{orangered}{\sin x\cos x})}{(\color{orangered}{\sin x\cos x})\cos x}\]

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0I follow now.. I think I get it. So, now that I have this ... (hold on)

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0\[1*\lim_{x \rightarrow \pi/4}\frac{1}{\cos(x)}\]

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0now that I have this, I just plug in pi/4?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So you were able to divide out "the problem piece", nice!

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0= \[(\sqrt{2})/2\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Hmm close. We're getting sqrt(2)/2, but that's in the denominator. And also, don't forget about your negative outside of the limit.

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0right, so the "final answer" is...

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{2}{\sqrt{2}}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Good, rationalize or simplify though

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0Ahhh... touche. I was wondering how my book had just negative sqrt.2... Got it, multiply top and bottom by sqrt.2, cancel out the 2's , and we get sqrt.2!! :D

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1wooo, nice job broski!

amonoconnor
 one year ago
Best ResponseYou've already chosen the best response.0Thanks again zepdrix! It's been a while, but your help is as helpful as ever!!
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