Is the function defined, continuous and differentiable

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Homework Help Overview

The discussion revolves around the properties of a piecewise function defined in terms of two variables, \( r_0 \) and \( B_0 \). Participants are examining whether the function is continuous and differentiable at a specific point, \( r = r_0 \).

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to graph the function as part of the analysis. There are questions about how to represent the variables \( r_0 \) and \( B_0 \) on the graph, indicating some confusion about their roles.

Discussion Status

The conversation is ongoing, with participants seeking clarification on how to graph the function and its components. Some guidance has been offered regarding labeling points on the axes, but there is no consensus on the approach to take for analyzing continuity and differentiability.

Contextual Notes

There appears to be uncertainty regarding the definitions and implications of the variables involved, which may affect the participants' ability to graph the function accurately. The original poster has expressed uncertainty about the appropriate method for determining differentiability.

Painguy
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Homework Statement


Graph the function defined by the following.
B = {(r/r0)B0 for r ≤ r0
{(r0/r)B0 for r > r0

(a) Is B continuous at r = r0?
yes no

(b) Is B differentiable at r = r0?

Homework Equations





The Attempt at a Solution



I'm not exactly sure what to do. I would use the definition of a derivative to do this, but I'm not sure if that's the right approach.
 
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What to do is start by following the instructions. It says "graph the function". Have you done that?
 
LCKurtz said:
What to do is start by following the instructions. It says "graph the function". Have you done that?

How would i graph r0 or B0? Its those two variables that confuse me.
 
Painguy said:
How would i graph r0 or B0? Its those two variables that confuse me.

Pick a point on the ##r## axis and label it ##(r_0,0)##. Similarly, label some point on the ##B## axis ##(0,B_0)##. Then draw the graph.
 

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