Hi, I'm new here and this is my first post but I'm having trouble with one of my homework problems. I have the function:
g(x) = (a(x+b)(x-c)(x+d)) / (e(x-f)(x-b)(x-c)), where a, b, c, d, e, and f are all unique, positive real numbers.
a) At what values of x=h does the limit g(x) = -∞ or +∞ as x->h?
b) Evaluate the limit of g(x) as x->c.
c) Does the limit g(x) as x->∞ exist?
I'm completely stuck and unsure where to start...
−∞−∞
Also, I was thinking about part c. Doesn't lim g(x) as x-> ∞ look for values where x is really large? If I expand the numerator and denominator I get:
(a(x^2+bx+dx+bd)) / (e(x^2-bx-fx+bf)), which for large x leaves me with ax^2/ex^2? Does that mean the limit exists and is a/e?
In limits NEVER JUST SUBSTITUTE!. Ask what happens near the limiting value?
If is near then is near .
Now for the last part. We play the 'back-of-the-book" game.
You look up the answer. You see: "the limit exists and equals ".
You may be scratching your head why? Can you explain why?
Ah ok, that makes sense. Well, I don't know if that's the right answer this is one of those problems that's not in the back of the book :P. I mean I understand I can reduce the fraction that way because when x is really large, x^2 is much more important than anything else in the equation. And when I have x^2/x^2 that just equals 1.