Use the definition of continuity to determine whether f is continuous at a.

f(x) = 5/(x + 5)
a = -5
A. Not continuous
B. Continuous

Question

Use the definition of continuity to determine whether f is continuous at a.

f(x) = 5/(x + 5)
a = -5
	A. Not continuous 	
	B. Continuous

anonymous · Answer

for a function to be conti  .... RHL = LHL = f(a)

anonymous · Answer

where 'a' is the point u check in

anonymous · Answer

I sort of understand. Can you show me how to plug everything in?

anonymous · Answer

I believe a continuous function is differentiable at all points correct? And in this case, it needs to be differentiable at a=-5. One way I determine this kind of problem is by visualizing it. You can see that as x approaches a, the function approaches infinity. When this happens, it can be said the function is not continuous at the point. Also, if you want to look at this by plugging in a for x, that's fine too. You would get:

5/0, which is roughly equal to infinity for our intents and purposes (since if we look at its values when x gets close to -5, the function gets extremely large with no bound).

If when you plug in a you get infinity, then it is not continuous. Hope that helps, but I can try to clarify if necessary.

anonymous · Answer

Oh and a bit of clarification,  that's only if it approaches infinity. Single point discrepancies do not count when considering continuity. In this case it was approaching infinity.

anonymous · Answer

That actually makes complete sense. I really get long explanations more then a I get formulas. Just giving me the formula makes me feel confused and stupid. -laughs- Now, I have a problem that's f(x) = x-4/x + 5 a = 4. I'm actually getting that that would be continuous?

anonymous · Answer

It looks continuous to me, since at a=5, the function is still defined. However, the function as a whole is not continuous, since at x=-5 the value is undefined. That is irrelevant though, since the question asks if it is continuous only at a=4. So yes, it is continuous at a=4. I can explain further, but it's a bit difficult to take from my mind and put it into words.

anonymous · Answer

Excuse me, the first sentence in my previous post should say "a=4".

anonymous · Answer

Nope, that actually makes perfect sense. I think I understand how to do it now. You're most excellent. Thanks again, Smokey!