Question

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.

Answer 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 ....

Answer 2

There are multiple x values then, x=-2.5; x=-1.5; x=-0.5; x=0.5; x=1.5;x=2.5

Answer 3

in the interval -3 to 3

Answer 4

So, you will have a range of values and not just one value in the solution

Answer 5

x={-2.5,-1.5,-0.5,0.5,1.5,2.5}

Answer 6

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?

Answer 7

It is possible to see it

Answer 8

Is there any point on the curve where , on drawing a straight line, you get a horizontal line ?

Answer 9

I can't see it, no. The x-axis itself?

Answer 10

This is one example