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 one year ago
An error exists in the logic that says the following. Explain where and why the error occurs and provide graphical support for your explanation.
 one year ago
An error exists in the logic that says the following. Explain where and why the error occurs and provide graphical support for your explanation.

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Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits \tan x dx = \int\limits \frac{ \sin x }{ \cos x } dx\]

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.0Set u =cos x, then du = sinx dx, so \(\int \dfrac{\sin x}{\cos x}dx=\int \dfrac{\sin xdx}{\cos x}=\int \dfrac{du}{u}\). Do you recognise what to do now?

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0i know i even get the answer \[\ln (\sec) + C\] But I can't find any error

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0read the question it says whts the error in converting tan to sin/cos

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.0Well, if I go on with what I started, I get lnu +C. If u > 0, this becomes \(\ln u + C = \ln u^{1} + C = \ln \frac{1}{u}+C=\ln(\sec x) + C\). If u < 0, you have \(\ln(u)+C=...=\ln(\sec x)+C\) So it is necessary to take into cosideration what sign tan x has.

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0we need calculus teachers here...not the correct answer

P0sitr0n
 one year ago
Best ResponseYou've already chosen the best response.0no brackets should be integral (sinx/cosx)dx

P0sitr0n
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits tanx dx = \int\limits (\frac{ sinx }{ cosx } )dx\]

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0cmon this is not the answer this doesn't even look like an error dude

P0sitr0n
 one year ago
Best ResponseYou've already chosen the best response.0lol just guessing maybe its this

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0dude i m frikin out lol

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.1I am unable to find a flaw in the logic only the math, you should end up with \[lncosx+C\] which you do after integration, I would assume this method approprite

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.1correction \[lncosx+C\]

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0ya so whats the error

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.1Whenever you do the u substitution integration technique it follows: let u=cosx du=sinx we then have\[\int\limits_{}^{}\frac{ 1 }{ u }du\] simply integrate from here the backsubstitute yielding \[lnu+C\] then \[lncos x+C\]

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0i know i know...i got this answer too...but i can't understand what is the error...read the question

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.1I did and there does not exist an error if it supplies a correct answer we use this trick a lot in higher exponential tangent casesI think though i may be wrong

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0it asks for the error in converting tan to sin/cos

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.1yes I understand but as I said I use this alot, I do not see the flaw in the logic provided the cosine function does not equal zero on your bounds

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0ok i guess...i said the same thing to my teacher but she said no there is one

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.1ha, really? that is odd. did you google it?

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0ya no help from there...google told me to come here haha

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.1lol ok well the only issue would be the graph contains asymptotes and DNE at multiple points aka cos x=0 but your domain should be restricted to allow for this. That would be my best guess as to the answer they are fishing for

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0what lol...say it again confused

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.1h/o a minute

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.1so if you look at the graph of the tangent function, it has horizontal asymptotes at every point where cos x=0 (shocking I know). Because cosine has a continuous domain and tangent does not, this must be accounted for whenever you evaluate a definite integral;however, your domain in a tangent function integration, usually accounts for this to start withunless they are being...not nice people.

Brotherman
 one year ago
Best ResponseYou've already chosen the best response.0lol...no idea to this man.....

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0haha...i am never gonna figure it out XD

Brotherman
 one year ago
Best ResponseYou've already chosen the best response.0I will copy it and show it to my lecturer and will get back to you

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0sweet...dont forget to get the equation from comment box

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0thx tell me ASAP plz

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0@amistre64 can u solve this

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0i cannot see a reason why there would be an error in that. By definition: \[\tan x=\frac{\sin x}{\cos x}\] is a trig identity. They have the same domains so reiterating the domain as Fibonacci pointed out ... seems moot. There is no error that can determine

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0.... that i can determine

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0haha...but there is an error idk wht

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.0@Best_Mathematician: A wide variety of Openstudy members have answered your question. The error you mention cannot be pointed out by any of them. I think it's your turn now. Just saying: there is an error is not enough. Ask your teacher what he/she means with the error. BTW: I am speaking out of experience: sometimes even teachers are wrong :) I know, because I'm a teacher myself...

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.0are you sure it does not say int tan x dx=int sin x dx/int cos x dx? Because that would be obviously flawed.

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.1@inkyvoyd ...that would make so much more sense

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0i m heck sure...the question i wrote is the exact same copy...and if it wud be like tht it wud be easy not challenging...and here i m asking challenging questions

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.1did you ask your instructor?

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.0The error is that "an error exists" itself then, I believe. Please ask your instructor :)

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0no worry... i will post the answer after my instructor replies...its spring break over here....but still i will reply the answer as soon as i can

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0just watch this question

Edutopia
 one year ago
Best ResponseYou've already chosen the best response.0There is no error in the OP. int(tanx)=int(sinx/cosx)=lnabs(secx)

Edutopia
 one year ago
Best ResponseYou've already chosen the best response.0maby your getting ln(abs(cosx)) but using the properties of logarithms this equals ln(abs(cos^(1)x)) = ln(abs(secx))

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0wrong answer

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0will reply the correct one asap

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0if anything, an error might exist in the assumption that an indefinite integration has a definite answer. \[\int tan(x)~dx=xxx+K\]\[\int \frac{sin(x)}{cos(x)}~dx=xxx+C\] but that distinction would be made pointless by the fact that an indefinite integral represents a family, or set, of functions anyway.
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