Use continuity to evaluate the limit.limx→π8sin⁡(x+sin⁡x)Don't really understand this. My trig func, knowledge is low but an explanation to look back to always helps me move forward.

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Use continuity to evaluate the limit.limx→π8sin⁡(x+sin⁡x)Don&#039;t really understand this. My trig func, knowledge is low but an explanation to look back to always helps me move forward.

Xyle1991 · Accepted Answer

&quot;Using continuity&quot; means use the fact that if f is continuous, then f(a)=limx→af(x). In your case f(x)=8sin⁡(x+sin⁡(x)) is continuous, so  limx→πf(x)=f(π)=8sin⁡(π+sin⁡(π))=8sin⁡(π)=0

George Burge · Accepted Answer

The phrase &quot; f is continuous at a&quot; really means  limx→af(junk)=f(limx→a junk)  Well, note quite. This is what &quot;f is continuous at whatever limx→a junk is.&quot;  So the start to your exercise is to write  limx→π8sin⁡(x+sin⁡x)=8sin⁡(limx→π(x+sin⁡x)).

Use continuity to evaluate the limit. \lim_{x\to\pi}8\sin(x+\sin x) Don't really understand this.

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