Wednesday, February 13, 2019

Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 41

Determine the value of the constant c that makes the function f(x)={cx2+2x if x<2x3cx if x2 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,


limx2cx2+2x=limx2+x3cxc(2)2+2(2)=(2)3c(2)4c+4=82c4c+2c=846c=4c=46=23


Therefore,
The value of c that would make the function continuous on (,) is 23

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