2.        Consider f(x) = `/`(`*`(sin(x)), `*`(x)); .  Does it have a discontinuity? Create a plot. If a discontinuity exists, highlight it on the image.  

restart;  

f := proc (x) options operator, arrow, function_assign; `/`(`*`(sin(x)), `*`(x)) end proc;  

f := proc (x) options operator, arrow; `/`(`*`(sin(x)), `*`(x)) end proc; (5.2.1)
 

f(0);  

Error, (in f) numeric exception: division by zero
 

 

 

iscont(f(x), x = -1 .. 1);  

false; (5.2.2)
 

 

 

`/`(`*`(sin(x)), `*`(x));  

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plot(f(x), x = -5 .. 5, y = -2 .. 2, discont = [showremovable]);  

Plot_2d