Consider the function f defined on [0,∞) f(x) = xrsin(1/x), for x≠0 and f(x) = 0, for x=0 where r > 0. Determine the range of r in which a) f is continuous on [0,∞) b) f is differentiable on [0,∞) c) f' exists and is differentiable on [0, ∞)

Consider the function f defined on [0,∞) f(x) = xrsin(1/x), for x≠0 and f(x) = 0, for x=0 where r > 0. Determine the range of r in which a) f is continuous on [0,∞) b) f is differentiable on [0,∞) c) f' exists and is differentiable on [0, ∞)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

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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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

Consider the function f defined on [0,∞)

f(x) = x^rsin(1/x), for x≠0 and f(x) = 0, for x=0 where r > 0. Determine the range of r in which

a) f is continuous on [0,∞)

b) f is differentiable on [0,∞)

c) f' exists and is differentiable on [0, ∞)

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