Sunday, 3 September 2017

Is it possible to solve limxtoafracsinxsinaxa without derivatives?

My teacher replaced xa=t and then said as x approaches a we have
aa=t so t approaches 0
and then said lim as t approaches 0, sin(t+a)sinat=limt0sintcosa+sinacostsinat and then she said that we apply limit only to sinacost so it becomes sinacos0 which is sina and then limt0sintcosa+sinasinat=limt0sintcosat as limt0sintt gives 1 so it is left cosa.




I was wondering if you can apply limit just to a part as she did. I know you can separate but if you separate then you get limt0sintcosat+limt0sinacosttlimt0sinat so its not the same as applying limit like that and separating because if you separate at limt0sinat if you apply limit it becomes sina0 so is it correct to do solve it as she did , I never seen it before so I am confused ?

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