Final answer:
The limit of 5/x sec(x) as x approaches pi/2 does not exist.
Step-by-step explanation:
To find the limit as x approaches pi/2 of 5/x sec(x), we can use the fact that the limit of a product is equal to the product of the limits. First, let's find the limit of 5/x as x approaches pi/2. As x gets close to pi/2, 5/x gets close to 5/(pi/2), which is equal to 10/pi. Next, let's find the limit of sec(x) as x approaches pi/2. The secant function is undefined at pi/2, so the limit does not exist at this point. Therefore, the overall limit of 5/x sec(x) as x approaches pi/2 does not exist.