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frx
Group Title
I have the function
\[f(x)=\frac{ \sin(x \pi ) }{ \sin(2x \pi) }\]
which is visually presented in the attached file.
I'm supposed, only by looking at the graph, to decide
* Where in the interval the function is discontinuous?
* Where does the curve have a horizontal tangent?
* Where does the function have local maximum, local minimum?
I can't see these things and would hence appreciate some guidance.
 one year ago
 one year ago
frx Group Title
I have the function \[f(x)=\frac{ \sin(x \pi ) }{ \sin(2x \pi) }\] which is visually presented in the attached file. I'm supposed, only by looking at the graph, to decide * Where in the interval the function is discontinuous? * Where does the curve have a horizontal tangent? * Where does the function have local maximum, local minimum? I can't see these things and would hence appreciate some guidance.
 one year ago
 one year ago

This Question is Closed

A_clan Group TitleBest ResponseYou've already chosen the best response.1
(1) By definition, An infinite discontinuity occurs when there is a vertical asymptote at the given x value. So, your x value will be ....
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
There are multiple x values then, x=2.5; x=1.5; x=0.5; x=0.5; x=1.5;x=2.5
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
in the interval 3 to 3
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
So, you will have a range of values and not just one value in the solution
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
x={2.5,1.5,0.5,0.5,1.5,2.5}
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
I get it, thanks! Then how about a horizontal tangent, don't I have to calculate the lim as f(x) goes to infinity or is it possible to see it?
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
It is possible to see it
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
Is there any point on the curve where , on drawing a straight line, you get a horizontal line ?
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
I can't see it, no. The xaxis itself?
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
dw:1365268526951:dw This is one example
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Are there two horizontal tangents then? Going through the points of the curvatures?
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
No, every point of curvature has its own tangent
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
So there are seven horizontal lines which are tangents but the question is asked in singular which should indicate that there where only one answer?
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
My experience is, In mathematics, the grammar of the question may not always indicate the quantity of solution.
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
So the solutionset is {3,2,1,0,1,2,3} then ?
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
yes, that looks right
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Great! What about the local maximum and minimum, there seems to be muliple max and mins too?
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
The solution to last part is situational. Local maximum and minimum may change depending upon the interval you choose for calculating them.
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
The interval is 3 to 3, like the graph shows
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
We say 'a' is local maximum if the height of the function at 'a' is greater than (or equal to) the height anywhere else in that interval.
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
In simple words, we can say, local maxima is the maximum height in certain part of the graph but if we consider the whole graph ,one of these has to be the 'global maximum'
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
dw:1365269863585:dw
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
A,B and C are the local maxima but out of these, B is the global maxima
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Sure i understand , so the local maximas are at 3, 1, 1 and 3 and the local mins are 2,0,2
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
That seems right
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Should I include the endpoints 3 and 3 according to WA they are not included http://www.wolframalpha.com/input/?i=Local+max+sin%28x+pi%29%2Fsin%282x+pi%29+from+3+to+3
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
It seems the local maxima and local minima are left out at the boundary because we do not have the values of y from both left side and right side,when x is approaching 3 or 3 .
 one year ago

A_clan Group TitleBest ResponseYou've already chosen the best response.1
Then correct solution should be 1 and 1
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Ok, that makes sense :)
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Thanks you so much for your help, really appreciate it!
 one year ago
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