I can't seem to get the hang of calculating these indeterminate forms...how do I figure out
limit ln(cosx) / ln(cos5x) as x goes to pi/2 from the left
The left limits of the numerator and denominator at pi/2 are negative infinity. So I tried looking at the limit of their derivatives: tanx / 5tan(5x) taking out the 1/5 I'm left to calculate the limit of tanx / tan5x. Once again the left limit at pi/2 is infinity.
So looking again at the limit of the derivatives it comes out (secx)^2 / 5(sec5x)^2
which once again I have no idea how to calculate.
I'm very confused.