I need step-by-step help for solving the lim x -> 0 for the function sin(x)/(x + tan(x))

Question

I can do simpler ones, but this one throws me off.

Thanks.

Answer 1

use L'Hopital's rule

lim sinx/(x + tanx) , as x---0
= lim cosx/( 1 + sec^2 x) as x --->0
= 1/(1+1)
= 1/2

test with your calculator:
enter .0000001 and store in memory of calculator
Make sure calculator is set to RAdians

evaluate:
RCL M
sin
=
÷
(RCL M
+
TAN
RCL M
)
=

you should get .5 or very close to .5

I use such a method for any limit question, to either check my answer or get a prediction of my answer

Answer 2

Perfect, thanks.