Determine the value of the constant c that makes the function f(x)={cx2+2x if x<2x3−cx if x≥2 continuous on (−∞,∞)
Based from the definition of continuity,
The function is continuous of at a number if and only if the left and right hand limits of the function at the same number is equal. So,
lim
Therefore,
The value of c that would make the function continuous on (-\infty, \infty) is \displaystyle \frac{2}{3}
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