7-5-85 variable in base and exponent
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CC
When evaluating this problem, we realize that K is in the base
and the exponent.
So we're going to take even the natural log of that thing.
We're going to bring down the exponent in front of the
coefficient using the power rule, and then we're going to
write that K that's in front as 1 / K in the denominator.
Now we can do Lopa Tau's rule because we can see that
currently it's an indeterminate form of 0 / 0.
So the derivative of the natural log is one over that, and then
the derivative of the inside in terms of K would be negative r /
K ^2.
The derivative of the denominator 1 / K is just -1 / K
^2.
So the -1 / K squareds are going to cancel, and it's going to
simplify to r / 1 + r to the K / K Well, when we're talking about
the limit as K goes to Infinity, R over Infinity is going to get
really, really small.
So we get r / 1 + 0.
Well, that's just R, so we get E to the R as our final answer.