Its just a general query about problems along these lines...
f(x)=|x^2+3x-18|/(x-3) and a =3, discuss the limiting behaviour of f(x) as x→a^+, as x→a^- and as x→a.
The Attempt at a Solution
So my basic solution to these types of problems are picking a number very close to 3 on either side of the number line, ie, 2.999 and 3.001 and then calculating to see what f9x) approaches given these values of x. The general answer I get is that x is negative on one side and positive on the other therefore as x→a the lim does not exist since lim x→a^- ≠ x→a^+. Although I have a test coming up and I know these types of questions are going to be involved, but I cant use a calculator in tthe test.
So my question is, do I need to state what f(x) approaces from both sides or is it sufficient to say its negative, then positive... therefore the lim does not exist.
The only reason I dont say what it approaches is because its hard to calculate ie what |(2.99999)^2 + 3(2.99999) -18|/ (2.99999 -3), is in my head.
so 1) do I need to state what it approaches... and 2) is there an easy way to calculate the squares and cubes etc of large decimal numbers is ie (2.99999999)^n?
Any help or thoughts greatly appreciated!