3. Consider the function g(x) defined by { x² sin(1/x) if x > 0, g(x) = if x <0. (a) Show that g(x) is continuous at r = 0. (b) Show that g(a) is differentiable at r = 0.
3. Consider the function g(x) defined by { x² sin(1/x) if x > 0, g(x) = if x <0. (a) Show that g(x) is continuous at r = 0. (b) Show that g(a) is differentiable at r = 0.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:3. Consider the function g(x) defined by
x² sin(1/x)
if x > 0,
g(x) =
if x < 0.
(a) Show that g(x) is continuous at x = 0.
(b) Show that g(x) is differentiable at x = 0.
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