what is the limit of this expression?

Question

lim as a --> 0 of ln (a) / -2a^2 ??

Answer 1

since top and bottom both tend to go to 0, use L'hoptal's rule

lim (a --> 0) ln (a) / -2a^2
= lim [d/da ln(a) / d/da ln (-2a^2)]
= lim ((1/a)/-4a)
=lim 1/-4a^2

as a-->0 lim --> negative infinity

Answer 2

lim as a->0 1/a ln a =1 standard form

the given expression can be changed to -[2/(a^2)lna]
=-[1/(a^2)ln(a^2)]
lim a->0 implies that if a^2=z then lim z->0
thus the modified expression becomes lim as z->0 -[(1/z)lnz]
=-1

hope this helps

Answer 3

as a=>0 from the right lna=>-infinitity
-2a^2 =>0 with a negative sign. so the quotient is positive and its limit is
+infinity

Answer 4

assuming you go from a>0 to the left,
ln (a) goes to - infinity
so all will go to +infinity