lim tan x-sinx/x 3 x--0
VIVIAN4:
in this lim is x tending to 0?
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I think your question is
lim (tanx- sinx)/x^3 x---> 0
you know if 0/0 limit gain then we differentiate both above and below w.rt x
now take this
lim (sec^2-cosx)/3x^2
we also gain 0/0 so again differentiate
so,
lim (2sec^2x.tanx+sinx)/6x
we again gain 0/0 but now we use
some concept
lim tanx/x =1 and lim sinx/x =1 when x->0
use this concept
hence lim (2sec^2x.(tanx/x) x+(sinx/x) x/6x=lim (2x+x)/6x=1/2
lim (tanx- sinx)/x^3 x---> 0
you know if 0/0 limit gain then we differentiate both above and below w.rt x
now take this
lim (sec^2-cosx)/3x^2
we also gain 0/0 so again differentiate
so,
lim (2sec^2x.tanx+sinx)/6x
we again gain 0/0 but now we use
some concept
lim tanx/x =1 and lim sinx/x =1 when x->0
use this concept
hence lim (2sec^2x.(tanx/x) x+(sinx/x) x/6x=lim (2x+x)/6x=1/2
please friends if you satisfy my answer mark as brainliest
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