Find the constant k that will make this piecewise continuous.by kaderyo94 Tags: constant, continuous, piecewise 

#1
Oct212, 10:34 AM

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1. The problem statement, all variables and given/known data
Find a value for the constant k that will make the function below continuous: [itex]f(x)=\frac{x1}{x^21}\ \text{if}\ x<=0[/itex] [itex]f(x)=\frac{tankx}{2x}~\text{if}~x>0[/itex] 2. Relevant equations 3. The attempt at a solution I've tried the only solution I can think of, which is to make [itex]\frac{x1}{x^21} = \frac{tankx}{2x}[/itex] And then I plug in 0 to try and get k, but I end up with 1 = 0/0. I know you are supposed to do something to the second equation to remedy this, but I cannot figure out what. I am fairly new to Calculus, so some help would be greatly appreciated. 



#2
Oct212, 11:36 AM

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Each piece of this piecewisedefined function has one or more discontinuities in its portion of the domain of the overall function. You can't "fix" those discontinuities by a choice of k. I suspect the problem is: Find a value for the constant k that will make the function continuous at x = 0, which is where the two "pieces" join. If that's the problem to be solved, then: What must be true for the following limit to exist? [itex]\displaystyle \lim_{x\to\,0}\,f(x)[/itex]Then, how must that limit be related to f(0) ? 



#3
Oct212, 05:22 PM

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You titled this "Find the constant k that will make this piecewise continuous" but then said "Find a value for the constant k that will make this function continous". Those are very different!



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