Friday, October 18, 2019

limits - limxrightarrow0fracsin(sinx)x



Can someone suggest how to solve this limit?


lim


If I substitute y=\sin x then \sin(\sin x)=\sin y while x=\arcsin y. Then the limit becomes \lim_{y\to 0}\frac{\sin y}{\arcsin y}


but this form is more complicated than the first one...


Answer



Hint multiply top and bottom by \sin x and break into a product of two limits.


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