Find the limits in Exercises 13–20. (If in doubt, look at the ...

Question

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)

17. lim(x→∞)arcsec(x)

Accepted Answer

Welcome back, everyone. Evaluate the limit. Limit as X approaches infinity of ar cosequant of 2 X A 0 B pi divided by 2, C, and D pi divided by 6. For this problem, what we're going to do is simply begin with the identity, and that would be arch co-sequent. Of 2 X is equal to arc of 1 divided by 2 X. So we're taking the reciprocal of 2 X, right? And this is valid as long as the absolute value of 2 X is greater than or equal to 1. We can apply that because X approaches infinity, right? So 2 X is going to be greater than or equal to 1. Meaning we can rewrite our limit as limit as x approaches infinity. Of Ark sign. Of 1 divided by 2 X. So now we have an outer function and an inner function. Using the properties of limits, we can simply rewrite it as arc sign off. The limit of the inner function. So limit as X approaches infinity of 1 divided by 2 X. Now, as X approaches infinity, our denominator is going to approach infinity, and we're dividing a constant by an infinitely large number. So our limit is going to be equal to 0, and we are simply taking our sign. Of 0. Let's recall that arc sign of 0 is 0, and this gives us the answer of a. Thank you for watching.

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)17. lim(x→∞)arcsec(x)

Watch next

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)
17. lim(x→∞)arcsec(x)