Find the following limits algebraically
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Find the following limits algebraically

Find the following limits algebraically

[From: ] [author: ] [Date: 11-10-11] [Hit: ]
the numerator is also 0 at x = 1. So the trick is to factor the numerator, cancel common factors, giving a rational function which is equal to the original one, except at x = 1, then use the same reasoning as worked on the problem you probably typed by mistake.......
lim x--->1 x^2+2x-3/x-1

-
If you really mean what you've written and the function whose limit you are taking is

x^2 + 2x - 3/x - 1

you have a rational function and are taking a limit at a point of its domain, so you can just plug the 1 in for x (since rational functions are continuous on their domain) and get 1 + 2 - 3 - 1 = -1

Unfortunately, I strongly suspect you meant to write

lim x--->1 (x^2 + 2x -3)/(x -1)

Again a rational function, but 1 is not in the domain since the denominator is 0 at x = 1. Fortunately, the numerator is also 0 at x = 1. So the trick is to factor the numerator, cancel common factors, giving a rational function which is equal to the original one, except at x = 1, then use the same reasoning as worked on the problem you probably typed by mistake.

So it becomes lim x--->1 (x-1)(x+3)/(x-1) = lim x--->1 (x+3) = 4.

(The first equation is true because a limit by definition only depends on what happens near the point being approached, in your problem 1. The second equation is true because for a rational function or polynomial, or more generally a continuous function, what happens to the value of the function as x approaches a point in the domain of the function, is it approaches the value of the function at the point.)

-
Is this
Lim (x² + 2x – 3)/(x – 1)?
x→1

If so, x² + 2x – 3 = (x – 1)(x + 3) so (x² + 2x – 3)/(x – 1) = (x + 3)/1

Therefore,

Lim (x²+ 2x – 3)/(x – 1) =
x→1

Lim (x + 3) = 4
x→1

You could apply l’Hopital’s rule, but the result is the same.

-
x² + 2x - 3 simplifies to....

(x+3)(x-1)

Knowing that....

lim x---> 1: (x+3)(x-1) / (x-1)

Like terms cancel...

lim x---> 1: x-3

Plug in 1 for x...

Final Answer:
4
1
keywords: algebraically,the,limits,following,Find,Find the following limits algebraically
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .