Help, Please? (Question Down Below)

P(x) = (x^4-2x^2-1)/(2x-1)

What Is P(1/2)?

Thank You!

1 Answer
Mar 2, 2018

Input 1/2 instead of x in the function:

(x^4-2x^2-1)/(2x-1)

becomes:

((1/2)^4-2*(1/2)^2-1)/(2*1/2-1)

=(1/8-(2*1/4)-1)/(1-1)

=(1/8-1/2-1)/(1-1)

=-1.375/0

What do we have here!? We can't divide by zero!

As you can see, the function makes no sense. At the instantaneous point of x=1/2, the value of y will ascend to infinity, and is not seen on a graph.

This is what we call an asymptote. The limit of the function is not defined at the infinitesimally exact point of x=1/2.

If needed, use desmos.com to graph the function, and marvel at the amazing asymptote you get.