rangnekarmitali
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- Joined
- Jul 12, 2020
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I have a limit question that is the limit as x approaches 0 of tan(2x)/tan(pi x). I know that the limit exists I just don't know how to break it down. Are there rules that I'm forgetting?
How do you know that? What is the value of that limit?I have a limit question that is the limit as x approaches 0 of tan(2x)/tan(pi x). I know that the limit exists I just don't know how to break it down. Are there rules that I'm forgetting?
At first I thought the limit doesn't exist because I broke the limit down as (sin2x/cos2x)(cos pi x/sin pi x). I thought that since as x approaches zero, sinx approaches zero as well, which would make the limit approach infinity times sin2x/cos2x. When I went to check my answer in the textbook, it said that the limit is 2/pi. I have to solve this limit without L'Hopital's rule, but I don't know how to move on from here.I have a limit question that is the limit as x approaches 0 of tan(2x)/tan(pi x). I know that the limit exists I just don't know how to break it down. Are there rules that I'm forgetting?
Hint:At first I thought the limit doesn't exist because I broke the limit down as (sin2x/cos2x)(cos pi x/sin pi x). I thought that since as x approaches zero, sinx approaches zero as well, which would make the limit approach infinity times sin2x/cos2x. When I went to check my answer in the textbook, it said that the limit is 2/pi. I have to solve this limit without L'Hopital's rule, but I don't know how to move on from here.
Oh ok, thank you!Hint:
\(\displaystyle \lim_{a\to 0}\frac{tan(a)}{a} \ = 1 \)
Write the given Left_Hand_side as product of two functions - each resembling the LHS of the equation above.
If you get stuck on the way - do come back and show your work. We will unstuck you!Oh ok, thank you!