Reasoning (1 Viewer)

leehuan

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Posting this in the 2U section as it's still within the scope of the course (even though it's just my homework).



I have the graph in front of me so I can pretty much infer the answer from just that. But say I wanted to do the following question without it.



Would the following method work:


_____________________________

Another question. Is this acceptable to find the limit as x approaches 3 from above (right)

 
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InteGrand

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Posting this in the 2U section as it's still within the scope of the course (even though it's just my homework).



I have the graph in front of me so I can pretty much infer the answer from just that. But say I wanted to do the following question without it.



Would the following method work:


_____________________________

Another question. Is this acceptable to find the limit as x approaches 3 from above (right)

I can't see the graph (actually, realised now it was for the function whose formula was given), but if the slope (namely [f(x) – f(3)]/(x – 3) ) approaches 2 from either side and f is continuous there (In fact, if [f(x) – f(3)]/(x – 3) approaches 2 (or some other finite number in general) from either side, then this actually implies that f is continuous there), then yes, f'(3) = 2. What you said is correct too, due to the result proved here: http://math.stackexchange.com/quest...nction-has-a-limit-must-it-agree-with-that-li.

And yes, the answer is 0 for the other limit Q.
 
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