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- 2 years ago
Lim. x → 1: [(x² + x - 2)/(x² - 1)]

By reason of factorisation, we have

Lim. x → 1: [(x + 2)(x - 1)/(x + 1)(x - 1)]

= Lim. x → 1: [(x + 2)/(x + 1)]

By direct substitution, we have

(1 + 2)/(1 + 1)

= 3/2

Therefore, Lim. x → 1: [(x² + x - 2)/(x² - 1)] = 3/2 ...Ans.

- khalilLv 72 years ago
you did mention ...where the x goes

if x → 1 then the f(1) → 0/0

hopital rule ... der top / der bottom

(2x + 1) / 2x

x → 1

the answer is 3/2 ◄◄◄

▬▬▬▬

if x → ∞ then

coefficient of higher on the top / coefficient of higher on the bottom

1/1

the answer is 1 ◄◄◄

- ted sLv 72 years ago
x² + x -2 = [x + 2 ] [ x - 1 ] & x² - 1 = [ x + 1 ] [ x - 1 ]...thus the ratio approaches 3/2 as x approaches 1

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- davidLv 72 years ago
If you want the limit as x approaches infinity, then you are correct

... Limit (as x -->infinity) of [X2+x-2/x2-1] = 1

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