Saturday, December 24, 2016

calculus - How do I find limlimitsxto0xcot(6x) without using L'hopitals rule?

How do I find limx0xcot(6x) without using L'hopitals rule?



I'm a freshman in college in the 3rd week of a calculus 1 class. I know the limx0xcot(6x)=16 by looking at the graph, but I'm not sure how to get here without using L'hopital's rule.




Here is how I solved it (and got the wrong answer). Hopefully someone could tell me where I went wrong.



limx0xcot(6x)=(limx0x)(limx0cot(6x))=(0)((limx0cos(6x)sin(6x))=(0)(10). Therefore the limit does not exist.



I am also unsure of how to solve limx0sin(5x)7x2 without using L'hopital's rule.

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