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I have been trying to work with limits and i came across a problem where it was defined that the limit for Sin(1/x) is not defined at x=0. Well i completely understand that part because the function oscillates for any small limit near 0. But i don't really understand how to calculate the limit for x for example at 0.1. Because the function still oscillates and what would be the ideal limit value that i need to take so that the function will proceed towards value sin(1/0.1)? And how to calculate similarly for sin(1/x^2), sin(1/x^3) etc until Sin(1/x^n) for x=0.1 from the definition of limits.

I tried to do a matlab code and generate graph to see if there is a pattern in oscillation, but unfortunately i could not decode anything. I have attached the graph here, the blue curve indicates sin(1/x), red for sin(1/x^2), green for sin(1/x^3) and black for sin(1/x^4).

P.S: In my opinion i felt this problem does not fall into homework questions, but i'm extremely sorry if someone else feels that way

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# Limits for Sin(1/x^n)

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