Question

please help me with this, i have to do it without using l'hospitals rule.
lim x->0 (sin(tgx)-tg(sinx))/(arcsin(arctgx)-arctg(arcsinx))

Answer 1

whats tg ? tan or tangent >?

Answer 2

tan

Answer 3

lets try numerator
tan x {sin(tan x)/tan x} - sin x {tan (sin x)/sin x}
use lim x->0 sin x/x = 1, lim x->0 tan x/x=1

Answer 4

so numerator simplifies to lim x->0 (tan x - sin x)

Answer 5

similarly denom simplifies to lim x->0 (arctan x -arcsin x)

Answer 6

so we have lim x-> 0 (tan x (1-cos x))/ (arctan x -arcsin x)
not sure how to proceed
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