Example 4 Video Example
Prove that -(sinh-l(x)) =
dx
√1+x²
Solution 1
Let y
sinh (x). Then sinh(y) = x. If we differentiate this equation implicitly with respect to x, we get
1.
dx
Since cosh?() - sinh?(y) = 1 and cosh(y) 2 0, we have cosh(y) - 1 + sinh?(y), so
1
dy
dx
1
cosh(y)
V1 + sinh?v)
Solution 2
we have
From the equation sinh-+(x) = \n(x + V x2 + 1).
-(sinh 'x) - 4 n(x + 2 + 1)-- --4(x + x + 1)
dx
- ** V*2+1 ( + vota)-
√²+1+x
1+1
+ 1
1

Suppose that 3% of all athletes are using the endurance-enhancing hormone epo (you should be able to simply compute the percentage of all athletes that are not using epo). for our purposes, a “positive” test result is one that indicates presence of epo in an athlete’s bloodstream. the probability of a positive result, given the presence of epo is .99. the probability of a negative result, when epo is not present, is .90. what is the probability that a randomly selected athlete tests positive for epo? 0.0297