SOLUTION: Graph the function f(x) = x+sqrt(abs(x)). Consider the behavior of the function at the point (-1,0) and at the origin. Find the limit as x approaches -1 and as x approaches 0. What

Algebra ->  Rational-functions -> SOLUTION: Graph the function f(x) = x+sqrt(abs(x)). Consider the behavior of the function at the point (-1,0) and at the origin. Find the limit as x approaches -1 and as x approaches 0. What      Log On


   



Question 1023344: Graph the function f(x) = x+sqrt(abs(x)). Consider the behavior of the function at the point (-1,0) and at the origin. Find the limit as x approaches -1 and as x approaches 0. What is different about the behavior of f(x) near those points? Explain. Next, graph its derivative. Discuss differentiability at -1 and 0.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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Function is continuous at x=-1 and continuous at x=0
lim%28x-%3E-1%2Cf%28x%29=0%29
lim%28x-%3E0%2Cf%28x%29=0%29
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Derivative is,
dy%2Fdx=x%2F%282%2Aabs%28x%29%5E%283%2F2%29%29%2B1
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Derivative is continuous at x=-1 and discontinuous at x=0
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