For what value of the constant c is the function f continuous on (−∞,∞) ? f(x)={cx2+9xx3−cx​ if x<6 if x≥6​ Part 1 of 2

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For What Value Of The Constant C Is The Function F Continuous On F X Cx2 9xx3 Cx If X 6 If X 6 Part 1 Of 2 1 (23.66 KiB) Viewed 32 times

For what value of the constant c is the function f continuous on (−∞,∞) ? f(x)={cx2+9xx3−cx​ if x<6 if x≥6​ Part 1 of 2 Note that f is continuous on (−∞,6) and (6,∞). For the function to be continuous on (−∞,∞), we need to ensure that First we find the left limit: x→6−lim​f(x)=x→6−lim​(cx2+9x)= Next, we find the right limit. x→6+lim​f(x)=x→6+lim​(x3−cx)=