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:
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.
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.