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anonymous
 one year ago
Friends please if you can help me with this exercise, this came into my calculus test 1: parameters found for "w" and "n" the equation cos (wx)  x / n has a real solution and calculate how many second solutions has exactly ..... please still do not know how to solve it thanks
anonymous
 one year ago
Friends please if you can help me with this exercise, this came into my calculus test 1: parameters found for "w" and "n" the equation cos (wx)  x / n has a real solution and calculate how many second solutions has exactly ..... please still do not know how to solve it thanks

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perl
 one year ago
Best ResponseYou've already chosen the best response.1The directions are somewhat unclear. Are you quoting word for word?

perl
 one year ago
Best ResponseYou've already chosen the best response.1Is this the equation : \( \Large \cos (wx)  \frac xn = 0 \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes that is the equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0search parameters of "w" and "n" for the equation has a real solution

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but also sought to find the exact number of solutions of the equation

perl
 one year ago
Best ResponseYou've already chosen the best response.1That's harder :) We can try using calculus

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This exercise was in my calculus test 1

perl
 one year ago
Best ResponseYou've already chosen the best response.1this problem is within the subject of calculus 1

perl
 one year ago
Best ResponseYou've already chosen the best response.1we can see that as n gets large \(\Large \cos (wx)  \frac xn \to \cos(wx) \)

perl
 one year ago
Best ResponseYou've already chosen the best response.1We could modify the equation \( \Large n\cdot \cos (wx) x = 0 \) The derivative is \( \Large n \sin(wx)w 1 = 0\) However I don't see how this helps

perl
 one year ago
Best ResponseYou've already chosen the best response.1Again just to be clear you want to know exactly how many real solutions are there to the equation: $$\Large \cos (wx)  \frac xn = 0$$ Does n have to be an integer? Clearly n=0 won't work.

perl
 one year ago
Best ResponseYou've already chosen the best response.1I don't see anything that pops out. @Michele_Laino @ParthKohli

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.1They call these things transcendental equations, don't they? Graphing is the way to go about these.

perl
 one year ago
Best ResponseYou've already chosen the best response.1yes . not an algebraic equation. i dont see any other way than by checking for sign change, using intermediate value theorem . but this does not give you a nice result

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0theorem of Bolzano or intermediate value theorem that thought but how to use it with the values of "w" and "n"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but forget to mention \[w >0,n \ge1\]

perl
 one year ago
Best ResponseYou've already chosen the best response.1we can assume n are integers. https://www.desmos.com/calculator/0pdovzb6kn

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think it has infinitely many solutions. As n goes larger, the continuity of the cosine (regarding W values) will ensure the existence of number k= cos (c) for some c in R such that k between (1,1). Now we can vary n in such a way that x/n is between (1,1) for any value of x (since n is independent). That is to say, for any x in the domain, there exist some n such that their ratio is between (1,1). on the other hand, we can change w as we want such that the equality still holds . in short, infinitely many solutions That's just what I think
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