Use analytical methods and/or a graphing utility to identify t...

Question

Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.

f(x)=1/ √x sec x

Accepted Answer

Welcome back, everyone. In this problem, we want to find the vertical asymptotes of the function F X equals 1 divided by X cubed and X. A says X equals K + 1 multiplied by pi where K is any integer. B says X equals a half of K pi where K is any integer. C says X equals 0, and the D says X equals Kpi where K is any integer. Now what do we know about vertical asymptotes? Well, we know it occurs where the denominator equals 0 if the numerator is not 0, OK? So let's go ahead and set the denominator equal to 0 and solve for X, and then let's see if it satisfies that condition in this case, for our tangent function, OK? So, setting the denominator to 0. Setting the denominator to 0 to solve for X, OK. Then We should find that we get X cube to turn X equal to 0. This tells us then that since this is a product that equals 0, either X cube equals 0 or a tangent of X equals 0. Now if X cubed equals 0, that means X equals 0. And if the tangent of X equals 0, that means X must be equal to k pi. In other words, it must be a multiple of pi for an integer k based on the period of the tangent. But no, since X equals 0 is within X equals k pi for K equals 0, then we can write the general solution as X equals k pi. Thus, the vertical asymptote is X equalskpi, where K is any integer. And we know it it won't make the numerator zero because our numerator is a constant. Therefore, D is the correct answer. Thanks for watching everyone. I hope this video helped.

Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.
f(x)=1/ √x sec x

Key Concepts

Vertical Asymptotes

Domain of a Function

Graphing Utility

Watch next