Question

Use continuity to evaluate the limit, as the limit of x approaches pi of 3sin(x+sinx)

Answer 1

\[\lim_{x \rightarrow \pi}3\sin (x+\sin x)\]

Answer 2

Use L'Hopital

Answer 3

@hba , l'hopital? what's that

Answer 4

Well you just diffrentiate it so that you don't end in a 0/0 form.This one looks simple so you'll have to just apply limit here.

Answer 5

hmm no just evaluate limit at pi

Answer 6

The function is continuous on all values of x.

Answer 7

That means that the limit of every x value is same as the y-value.
In other words, \[\lim_{x \rightarrow a}f(x)=f(a)\]
where a is a x-value on f(x)

Answer 8

So, \[\lim_{x \rightarrow \pi}3\sin(x+\sin x)=f(\pi)\]

Answer 9

Evaluate f(pi) and you'll get 0.