Calculus Help! lim x--->0 sin(3x) / (√2)x+tan(x) =.....

= 3(-1 + √2). thats the answer, I just need to know how to do the steps.

thanks in advance!!

lim x--->0 sin(3x) / (√2)x+tan(x) )
= 3 / (√2)+1 )
= 3((√2) -1 )
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Ideas: As x-->0, sin(3x) ~ 3x, tan(x) ~ x

Hi. I'm graduated on maths and i'm also teacher.

You have to divide the expression by 3x, then,

[ sen3x/3x) / [ V(2x)/(3x) +tgx/(3x)].

Now, knowing that tgu/u ->0 and senu/u ->0, the limit of the expression is 1/ [V2/3 + 1/3) = 3/(V2+1).