Answered: Let f(x) = { x^(2) - x if x is smaller…

Let f(x) = { x^(2) - x if x is smaller than or equal to 0, x[sin(pi+x)] if 0 < x} where [y] = greatest integer less than or equal to y. a) Is f continuous at 0? b) Is f differentiable at 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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Question

Let f(x) = { x^(2) - x if x is smaller than or equal to 0, x[sin(pi+x)] if 0 < x} where [y] = greatest integer less than or equal to y.

a) Is f continuous at 0?

b) Is f differentiable at 0?

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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