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,
limx→2−cx2+2x=limx→2+x3−cxc(2)2+2(2)=(2)3−c(2)4c+4=8−2c4c+2c=8−46c=4c=46=23
Therefore,
The value of c that would make the function continuous on (−∞,∞) is 23
No comments:
Post a Comment