create f(x) & pick a point c such that the limit of f(x) as x approaches c from both left and right are equal and continuous.show the values
show the values of the limits and explain why the function is continuous.The explanation should be intuitive as well as mathematical. include a graph of the function
f(x) = 5x.
The right limit as x--> c= Limit h-->0 5(c+h) = 5c
The left limit of 5x as x--> c = limit h-->0 5(c+h) =5c.
At x=c, function takes the value 5c.
Thus the the left limit = right limit = functional value at = c. This holds for all c belonging to R.
Thus thus 5x is an example for the typical function constructed.