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Question Number 192999 by Mastermind last updated on 01/Jun/23
Show that the following functions are continous on a close interval [0, 1]. f(x)={_(3 x=1) ^(((x^2 +x−2)/(x−1)) x≠1) Help!
Showthatthefollowingfunctionsarecontinousonacloseinterval[0,1].f(x)={3x=1x2+x−2x−1x≠1Help!
Answered by MM42 last updated on 02/Jun/23
lim_(x→0^+ ) f(x)=f(0)=2 lim_(x→1^− ) f(x)=lim_(x→1^− ) (((x−1)(x+2))/(x−1))=3 & f(1)=3 ∀c∈(0,1) ; lim_(x→c) f(x)=f(c) therfore ; f is continous on [0,1]
limx→0+f(x)=f(0)=2limx→1−f(x)=limx→1−(x−1)(x+2)x−1=3&f(1)=3∀c∈(0,1);limx→cf(x)=f(c)therfore;fiscontinouson[0,1]

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