My teacher replaced x−a=t and then said as x approaches a we have
a−a=t so t approaches 0
and then said lim as t approaches 0, sin(t+a)−sinat=limt→0sintcosa+sinacost−sinat and then she said that we apply limit only to sinacost so it becomes sinacos0 which is sina and then limt→0sintcosa+sina−sinat=limt→0sintcosat as limt→0sintt 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 limt→0sintcosat+limt→0sinacostt−limt→0sinat so its not the same as applying limit like that and separating because if you separate at limt→0sinat 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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