Calculus help

Question

Can someone help me with this problem, please?

 

f(x) = x^2 − 2x / x^2 − 4

 

Evaluate the function f(x) at the given numbers (correct to six decimal places).

 

x = 2.1, 2.05, 2.01, 2.001, 2.0001,
1.9, 1.95, 1.99, 1.999, 1.9999

Answer 1

This is a brute force question.

Use a spreadsheet like Excel and simply plug the required values into the spreadsheet.

 

However, what is being demonstrated here is that even though the function is undefined (0/0) and discontinuous at x = 2, it, in fact, has a so-called removable discontinuity at x = 2 and a limit of 1/2 at x = 2.  To see this factor the numerator and denominator and divide out the common factor.

 

It also has another essential discontinuity and vertical asymptote at x = -2.

Answer 2

You have a function f(x).  Just plug in the numbers where x appears in f(x).  It is just arithmetic.  Now be careful whether you mean

 

(x² - 2x)/(x² - 4)

 

or something else.  You need to group things in parentheses.