|Mar28-09, 04:00 PM||#1|
Continuity in general
OK. Starting with a basic question, can we determine whether a function is continuous in general?
So far, our tutorial questions were all about continuity/ discontinuity at a given point. I mean, we should firstly prove that the right-hand and the left-hand limits are equal (while x tends to c) and then the obtained value should be equaled to the value of function at the given point which is f(c).
For this question we have no “c” in fact. It IS asking for that “c”, to some extent.
The question: For what values of x is the function f(x) continuous?
|Mar28-09, 08:43 PM||#2|
|Mar29-09, 01:43 AM||#3|
Thanks for the response. I was also going to solve the question using an arbitrary value, but it says "For what VALUES of x", so most probably, there should be an interval of continuity for this function.
Let's show some effort. This is my answer:
The denominator shouldn't be zero. So, x cannot be +5 and -5.
The final value for the square root should not be negative. Therefore: x<-3 and x>+3
We can clearly deduct that we have infinite discontinuity in +5 and -5 and jump discontinuity in -3<x<+3.
Thus, the values of x in which f(x) is continuous: (-∞,-5); (-5,-3]; [+3, +5); (+5, +∞)
|continuity, functions, general, limit, point|
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