Calculus HELP? Please

[Vertigo-X]

Dark_Lord_2008 said:

Google it and you will find the answer.
lim x->0 sin(x)/x=1 lim x->0 1-cos(x)/x=0
http://answers.yahoo.com/question/index?qid=20080603183843AAHFO2l

lim->0 x+tan(x)/sin(x)

lim 1/ (x/sinx + tanx/sinx)

note:
lim sinx/x = 1
thus
lim x/sinx = 1

now, tanx / sinx = 1/cosx .
and lim (1/cos(x)) = 1, as x→0

thus
lim sinx/(x+ tanx) = 1/(1 + 1) = 1/2
(Is that the trig proof and answer?)

That shouldn't work, either. I could be wrong, but this equation can be simplified further than it's original form:

 

lim x->0 x+tan(x)/sin(x)

lim x->0 x + [sin(x)/cos(x)]/sin(x)

lim x->0 x+ 1/cos(x)

Going straight up by your own rules, lim x->0 (0 + 1/1) = 1

 

EDIT: The thought occurred to me that I may have misinterpreted your equation. It should be written like this if x + tan(x) is the numerator:

lim x->0 [x+tan(x)]/sin(x)

 

EDIT2: In the case of that being your equation, I don't understand why you flipped the original limit in your work. The way I'd do it is:

 

lim x->0 [x+tan(x)]/sin(x)

lim x->0 [x/sin(x) + tan(x)/sin(x)]

lim x->0 x/sin(x) + lim x->0 tan(x)/sin(x)

(           1           ) + lim x->0 1/cos(x)

(1) + (1) = 2