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.

g(θ)=tan πθ/10

Accepted Answer

Welcome back, everyone. In this problem, we want to find the vertical asymptotes of the function P of Z equals the tangent of pi Z divided by 15. A says Z equals 1. 15 + 5k where K is any integer. B says it's 2/15 plus 5k. C 1/2 of 15 + 15k, and D 15 + 1/2 of 15k. In all cases where K is any integer. Now how are we going to find the vertical asymptote of PF Z? Well, notice that PF Z is a tangent function. So we must determine where the tangent function is undefined to find the vertical asymptotes. Recall that the tangent function is undefined where its argument is half of pi plus K pi, OK? In other words, let's write a thought here. Tangent function is undefined. OK. Where It's argument, OK. We're sorry, Intan Theater. The its argument would be equal to a half of pi plus k pi. So to figure out what makes the tangent of pi Z divided by 15 undefined, we can equate it to the condition that makes it undefined. In other words, we can set pi Z divided by 15 to 1/2 of pi plus k pi, where K is an integer. If we solve for a Z, OK, notice that we can cancel pi from all terms, OK. And then uh we can multiply both sides by 15 and thus that will give us a value for z to be equal to half of 15 plus 15k where k is any integer. Therefore, that means C. Is the correct answer. Thanks a lot 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.g(θ)=tan πθ/10

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Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.
g(θ)=tan πθ/10