MATHEMATICS: LIMITS

Thursday, May 7, 2020

Why is the limit as x approaches positive or negative infinity of the function ƒ(x) = (x+1) /(x-2) equal to 1?

f(x)=(x+1)/(x-2) when x→∞

if we put x=∞ then it is ∞/∞ form

or if let x=1/t then t→0

f(1/t)=(1/t+1)/(1/t-2) when t→0

or f(1/t)=(1+t)/(1-2t) when t→0

or t=0, f(1/t)=(1+0)/(1-2×0)=1

hence proved