Asked by Linda Zakay
suppose f(x) = {x-1/x^4-1 if x <= 2 and |x-3|/x-3 if 2<x
Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities.
Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities.
Answers
Answered by
oobleck
(x-1)/(x^4-1) = 1/((x+1)(x^2+1)) for x≠1
There is a hole at x=1
|x-3|/(x-3) = 1 if x>3
= -1 if x<3
So there is a hole at x=3
lim(x→2-) f(x) = 1/15
lim(x→2+) f(x) = -1
So there is a jump discontinuity at x=2
There is a hole at x=1
|x-3|/(x-3) = 1 if x>3
= -1 if x<3
So there is a hole at x=3
lim(x→2-) f(x) = 1/15
lim(x→2+) f(x) = -1
So there is a jump discontinuity at x=2
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