Posted by Derrick on Friday, September 16, 2011 at 3:17pm.
For what values of a and b that make the function f continuous everywhere.
f(x)={(x^24)/(x2) if x<2
ax^2bx18 if 2<x<3
10xa+b if x>3

calculus  MathMate, Friday, September 16, 2011 at 4:31pm
There are three segments of functions, and two possibly discontinuous points, at x=2 and x=3.
Equate the adjacent segments to find the value of a and b that make the segments have the same values at x=2 and x=3.
Finally, check that the limits approaching from each side (2 and 2+, 3 and 3+) of the combined function are identical. They should be if the function is continuous.
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