2020-02-19 09:08 Continuity& Differentiability miscellaneous online topics for Calculus Applied to the Real World Part A: Continuity Return to Main Page You can now either go on and try those exercises that deal with continuity in the exercise set for this topic, or first finish the online text by going to Part B: Differentiability. Return to Main Page
Continuity and Differentiability If this condition is not satisfied, we say that the function f is discontinuous at a. This situation could arise in several different ways. Differentiability We have earlier seen functions which have points at which the function is not differentiable. An easy example is the absolute value function which conditions that destroy differentiability
Conditions that destroy Differentiability. 1)discontinuities in the graph 2)corners in the graph 3)cusps in the graph (the slope approached positive infinity on either side) 4)vertical tangents in the graph. Differentiability implies continuity. if it is differentiable at xc then it is continuous at the point.
Conditions that Destroy Differentiability 155 165 (2. 8) Corner Cusps Vertical tangent lines Discontinuities Answer both parts below for f (x) a) Show thatJ(x) is or is not continuous at x 0. b) Prove thatJ(x) is or is not differentiable at x 0. is 2. The graph shown below has a vertical tangent at (2, 0) and horizontal tangents at (1, conditions that destroy differentiability
(Jupyter Notebook) and (SageMath Worksheet). So far we have looked at derivatives outside of the notion of differentiability. The problem with this approach, though, is that some functions have one or many points or logo1 CauchyRiemann EquationsPolar CoordinatesAnalytic FunctionsHarmonic Functions Equivalent Conditions for Differentiability Bernd Schroder Bernd Schroder Louisiana Tech University, College of Engineering and Science Continuity& Differentiability miscellaneous online topics for Calculus Applied to the Real World Part B: Differentiability Return to Main Page Part A: Continuity Exercises for This Topic Index of OnLine Topics Everything for Calculus Everything for Finite Math Everything for Finite Math& Calculus Utility: Function Evaluator& Grapher conditions that destroy differentiability Jun 28, 2010 Condition for differentiability Jun 27, 2010# 1. Mano Jow. What's the condition for f(x, y) to be differentiable in its domain? I googled for it but couln't find Thanks in advance. Mano Jow, Jun 27, 2010. Phys. org latest science and technology news stories on Phys. org PTF# AB 14 Conditions that Destroy Differentiability Remember for a function to be differentiable, the slopes on the right hand side must be equal to the slopes on the left hand side. There are four conditions that destroy differentiability: 1. Discontinuities in the graph. (Function is not continuous. ) 2. Corners in the graph.
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