Question

breaking up a fraction into two, sin(x)/x+tan(x)

Answer 1

its better if there is a sum up top; otherwise it gets hairy

Answer 2

is there still a way to break it up though? I thought there was but I can't remember for sure.

Answer 3

decomp; but i got no idea how to do it for this; unless theres an add 0 trick

Answer 4

does sin(x)/x=1 help?

Answer 5

thats not an identity

Answer 6

lim n to inf for whole bit

Answer 7

is x+tan(x) the denom?

Answer 8

true, but can that be pulled out of the given fraction.....yes for denom ?

Answer 9

if you factor it out ....

\[\frac{sin(x)}{x}*\frac{1}{1+\frac{tan(x)}{x}}\]

Answer 10

tan(x)/x = sin(x)/xcos(x) so maybe

Answer 11

if we limit it; i believe it would go to:

\[\frac{1}{1+sec(x)}\]

Answer 12

no kidding right?, I knew it had to be something simple I was overlooking. Thanks for the help, I just needed the jolt. I appreciate it, you're the man.

Answer 13

http://www.wolframalpha.com/input/?i=limit%7Bx+to+0%7D+sin%28x%29%2F%28x%2Btan%28x%29%29

Answer 14

yep

Answer 15

wolf used Lhopital :)