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HOW TO FIND VALUES OF A AND B THAT MAKE F CONTINUOUS EVERYWHERE | Piecewise functions continuity
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How to find values of a and b that make f continuous everywhere. This will follow the same process as any other problem where you need to find a and b that make a piecewise function continuous everywhere. Piecewise functions continuity can be tricky at times, but if you follow this process you should be able to find a and b that make a piecewise function continuous everywhere. This problem will be unique because the answer may look a little different than you're used to.
0:00 How to find values of a and b that make f continuous everywhere
0:24 The definition of continuity
2:02 Set up equations to make f continuous at x=1
4:52 Evaluate the limits
6:30 Simplify your equation(s)
We will need to use the definition of what it means for a function to be continuous at a point in order to make sure this piecewise function is continuous at the point where it switches from one piece to the other.
If we know that each piece is a linear or quadratic function regardless of the constants a and b, then we can forget about making sure each piece in continuous on its own domain and apply this shortcut. Here I'll show you the quick and easy way to find the value of the values of a and b that will make the piecewise function continuous everywhere.
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0:00 How to find values of a and b that make f continuous everywhere
0:24 The definition of continuity
2:02 Set up equations to make f continuous at x=1
4:52 Evaluate the limits
6:30 Simplify your equation(s)
We will need to use the definition of what it means for a function to be continuous at a point in order to make sure this piecewise function is continuous at the point where it switches from one piece to the other.
If we know that each piece is a linear or quadratic function regardless of the constants a and b, then we can forget about making sure each piece in continuous on its own domain and apply this shortcut. Here I'll show you the quick and easy way to find the value of the values of a and b that will make the piecewise function continuous everywhere.
READ MORE
WATCH NEXT
YOU MIGHT ALSO BE INTERESTED IN...
Some links in this description may be affiliate links meaning I would get a small commission for your purchase at no additional cost to you.
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