Question
Find the limit: lim x-> 2 ln(x/2)/ (x^2−4)
Can someone help me with this?
Can someone help me with this?
Answers
Catherine
I thought that it was 1/4 but that's now the answer....
Catherine
What I thought that I had to do was to take the derivative, (2/x)/2x and then plug in 2... and that's how I got 1/4, but that's not the answer, what do I have to do?
MathMate
D'hôpital's rule works here.
The expression is
ln(x/2)/ (x^2−4)
not
2ln(x/2)/ (x^2−4)
as it appears in the post.
The leading 2 belongs to the limit of x.
Differentiate both top and bottom with respect to x:
Lim (1/x) / (2x)
= lim 1/(2x²)
=1/(2(2)²)
=1/8
The expression is
ln(x/2)/ (x^2−4)
not
2ln(x/2)/ (x^2−4)
as it appears in the post.
The leading 2 belongs to the limit of x.
Differentiate both top and bottom with respect to x:
Lim (1/x) / (2x)
= lim 1/(2x²)
=1/(2(2)²)
=1/8