Knownothing
Knownothing Knownothing
  • 26-01-2019
  • Mathematics
contestada

Need help with this continuity problem.

Need help with this continuity problem class=

Respuesta :

LammettHash
LammettHash LammettHash
  • 26-01-2019

In order to be continuous everywhere, we only need to satisfy continuity at [tex]x=10[/tex]. For that to happen, we need to have

[tex]\displaystyle\lim_{x\to10^-}f(x)=\lim_{x\to10^+}f(x)=f(10)[/tex]

By the function's definition, [tex]f(10)=2(10)-2=18[/tex]. Compute the limits:

[tex]\displaystyle\lim_{x\to10^-}f(x)=\lim_{x\to10}2x-2=18[/tex]

[tex]\displaystyle\lim_{x\to10^+}f(x)=\lim_{x\to10}-8x+b=-80+b[/tex]

So we must have

[tex]18=b-80\implies b=98[/tex]

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