Calculus Problem I am Stuck On

[GreenHeron]

Let f(x) = (x² - 5x + c)/(x²(2x-4)). For x = 0 and x = 2, find the accompanying values of the constant c such that lim x -> c f(x) does NOT exist. (Each x-value should have its own unique c-value.)

 

[HallsofIvy]

Saying "x= 0 and x= 2" and then "lim x-> c" makes no sense!

I suspect that, if you go back and read the problem again, you will find that the limits are as x goes to 0 and as x goes to 2.

For a continuous function, f(x), the limit as x goes to a, is just f(a). I suggest you set x= 0 and see what c must be so that the limit does not exist, then do it again with x= 2.