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frx
 2 years ago
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.
frx
 2 years ago
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.

This Question is Closed

A_clan
 2 years ago
Best 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 ....

frx
 2 years ago
Best ResponseYou've already chosen the best response.0There are multiple x values then, x=2.5; x=1.5; x=0.5; x=0.5; x=1.5;x=2.5

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

A_clan
 2 years ago
Best ResponseYou've already chosen the best response.1x={2.5,1.5,0.5,0.5,1.5,2.5}

frx
 2 years ago
Best ResponseYou've already chosen the best response.0I 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?

A_clan
 2 years ago
Best ResponseYou've already chosen the best response.1It is possible to see it

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

frx
 2 years ago
Best ResponseYou've already chosen the best response.0I can't see it, no. The xaxis itself?

A_clan
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1365268526951:dw This is one example

frx
 2 years ago
Best ResponseYou've already chosen the best response.0Are there two horizontal tangents then? Going through the points of the curvatures?

A_clan
 2 years ago
Best ResponseYou've already chosen the best response.1No, every point of curvature has its own tangent

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

A_clan
 2 years ago
Best ResponseYou've already chosen the best response.1My experience is, In mathematics, the grammar of the question may not always indicate the quantity of solution.

frx
 2 years ago
Best ResponseYou've already chosen the best response.0So the solutionset is {3,2,1,0,1,2,3} then ?

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

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

frx
 2 years ago
Best ResponseYou've already chosen the best response.0The interval is 3 to 3, like the graph shows

A_clan
 2 years ago
Best ResponseYou've already chosen the best response.1We 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.

A_clan
 2 years ago
Best ResponseYou've already chosen the best response.1In 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'

A_clan
 2 years ago
Best ResponseYou've already chosen the best response.1A,B and C are the local maxima but out of these, B is the global maxima

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

frx
 2 years ago
Best ResponseYou've already chosen the best response.0Should 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

A_clan
 2 years ago
Best ResponseYou've already chosen the best response.1It 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 .

A_clan
 2 years ago
Best ResponseYou've already chosen the best response.1Then correct solution should be 1 and 1

frx
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks you so much for your help, really appreciate it!
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