Help me please? I am getting confused by these one sided limits, and the text ihave just lightly touches this topic.
The question is : Use L'Hopital's Rule to find the limit:
and
What i didn't understand was the example in my text about this. It says that Why is this? I am a bit confused by the one-sided limits...
for the second limit just use L'Hospital's Rule. As for your question on the bottom, make sqrt(x)ln(x) into the equivalent fraction ln(x) / 1/sqrt(x). then use L'Hospital's Rule and you get 1/x / (-1/2)x^(-3/2), using the laws of exponents, when you divide two terms with like bases you subtract the powers so -1 - (-3/2) = 1/2 and 1 / (-1/2) becomes -2 so finally your expression now should looke like -2sqrt(x) and if you plug in 0, you get the limit as 0.
For this one, i guess. But honestly, the one-sided limit concept is very unclear to me, and i guess some of the limit rules associated with that and some trig functions and so. And the resourses i have are a bit limited, so I am not getting a clear pic at all. Then came this L'Hopital and Newton rules that I havent gotten much of either, which is just compounding what i don't know. I can't even understand the example in the book. See my 1st post on this thread. I quoted an example from my text. Can you explain that to me please?
Understand that is undefined for negative values, so doesn't make any sense. But makes perfect sense. We are still concerned with the behavior of as , but we haven't made a s non-sensical statement.
Do you understand?
As for the example itself...
gives the indeterminant form , so rewriting we have
which now produces .We apply L'Hopital's rule and we have
Which is what your text has.
Thanks. The text does have those steps, but my problem was just about the substitution of the 0 since it was a one sided limit. I wasn't sure that you could've simply plugged in the zero even though we are concerned with values above zero. But you explanation of that makes it clearer. Thanks. The other steps before i understood.
thanks.
you're looking for what the function approaches as x approaches 0 from the right. if it will help you see, make a table of values and see what happens to the function when you plug in numbers approaching 0 from the right. you can also graph the function and observe the behavior as x approaches 0 from the right. when dealing with symbols, just plug in the number 0 since most of the time the limit as x approaches some some value is equal to the function evaluated at that value.