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Calculus/Intervals of Continuity...

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Expert: - 1/31/2008


Question
I have trouble with trig functions and I cant figure this out.  f(x)= (cos(x))/(sqrt(x-10)).  I cant figure out the intervals of continuity for this one.  I thought it would be (-infinity, 10) U (10, Infinity).

Answer
There are two factors to check for continuity.  One of them is division by zero and the other is which x can be put in the equation.  

For cos(x), the function can have any value for x and is in the numerator, so 0 values are no problem.

For sqrt(x-10), x-10 must be positive (x-10)>=0, but x-10 can't be zero, so (x-10)>0.

As long as we only allow real numbers to occur, the set of numbers on which this function is defined is (10,infinity).  If complex numbers are allowed, you have the right answer.

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