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41. Show that f(x) = 3√x is continuous at x = 0 but not dif- ferentiable at x = 0. Sketch the graph of f.

41. Show that f(x) = 3√x is continuous at x = 0 but not dif- ferentiable at x = 0. Sketch the graph of f.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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#41, use limit definition of deriv

mee hif- be me nd of b. ban of functions that are not differentiable, and explain the relationship between differentiability and continuity. 41. Show that f(x) = 3x is continuous at x = 0 but not dif- ferentiable at x = 0. Sketch the graph of f. 3 42. Show that f(x) = √(x - 2)² is continuous at x = 2 but not differentiable at x = 2. Sketch the graph of f.T.E 43. Show that f(x) = = x² +1, x ≤ 1 X 12.x, x > 1 is continuous and differentiable at x = 1. Sketch the graph of f. ^^ Show that
Transcribed Image Text:mee hif- be me nd of b. ban of functions that are not differentiable, and explain the relationship between differentiability and continuity. 41. Show that f(x) = 3x is continuous at x = 0 but not dif- ferentiable at x = 0. Sketch the graph of f. 3 42. Show that f(x) = √(x - 2)² is continuous at x = 2 but not differentiable at x = 2. Sketch the graph of f.T.E 43. Show that f(x) = = x² +1, x ≤ 1 X 12.x, x > 1 is continuous and differentiable at x = 1. Sketch the graph of f. ^^ Show that
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