Question

Problem 3 in attached image

Problem 3 - Let g(x) and h(x) be the following piece-wise defined functions
x1, if x<0
if 0 1
g(ax)
IC
2 , if 1 <x
1, if x < 0
h(ar) =
if 0 x 1
In x,
2 x, if 1 << x
a) Find the points where g(x) is discontinuous
b) At which of these points is g(x) right-continuous, left-continuous or neither?
c) State the type of discontinuity at these points (removable, jump, or infinite)
d) Repeat a), b), c) for h(x)

Image Transcription

Problem 3 - Let g(x) and h(x) be the following piece-wise defined functions x1, if x<0 if 0 1 g(ax) IC 2 , if 1 <x 1, if x < 0 h(ar) = if 0 x 1 In x, 2 x, if 1 << x a) Find the points where g(x) is discontinuous b) At which of these points is g(x) right-continuous, left-continuous or neither? c) State the type of discontinuity at these points (removable, jump, or infinite) d) Repeat a), b), c) for h(x)

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Math
Calculus

Continuity

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