Analyze general properties of continuity and discuss the continuity of the following. f(x)=3{x2−9}

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Analyze general properties of continuity and discuss the continuity of the following.  f(x)=3{x2−9}

hesgidiauE · Accepted Answer

To analyze and discuss the continuity of the given functions in each part: f(x)=3{x2−9} Note that for a function f(x) to be continuous at a point c it should satisfy: limx→c+f(x)=limx→c−f(x)=f(c) Now note that x2−9 is a polynomial that is continuous everywhere, since it satisfy above property. And the cube root function is also continuous everywhere so the function f(x)=3{x2−9} is also continuous everywhere. Since limx→c+f(x)=limx→c+3{x2−9} =limh→03{(c+h)2−9}=3{c2−9} limx→c−f(x)=limx→c−3{x2−9} =limh→03{(c−h)2−9}=3{c2−9}, and f(c)=3{c2−9} Thus, limx→c+f(x)=limx→c−f(x)=f(c)

Jeffrey Jordon · Accepted Answer

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Analyze general properties of continuity and discuss the continuity of the follo

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