Question

lim as x approaches 0 of tanx/x

Answer 1

I broke that down into the lim of sinx/(xcosx)

Answer 2

tan x = x + x^3/3 + x^5/15 .... smaller and smaller for x-->0

so
(1/x) tan x = 1 + x^2/3 + x^4/15 .....
which looks like one for small x

Answer 3

sorry i should have put lim tan(x)/x

Answer 4

I broke that down into the lim of sinx/(xcosx)

sin x --> x + x^3/3! + x^5/5! ...
cos x --> 1 -x^2/2! + x^4/4! ....

so
(x+ x^3/3! ...)
-----------------
(x -x/2! ....)

x/x

1

Answer 5

how did you get all of those x's with exponents?

Answer 6

The series for sine and cosine

Answer 7

The point is that tan x approaches x for small x and therefore (1/x)tan x becomes 1/1 or 1 as x goes to zero.