Question

Evaluate this limit

Answer 1

\[\huge \lim_{x \to 1}\frac{ x ^{3}-3x ^{2}+3x-1 }{ \tan(x-1) - \sin(x-1) }\]

Answer 2

have you attempted L'Hopital ?

Answer 3

not allowed... and the bottom is still 0 I think.

Answer 4

I trid to use identities at the bottom but. well we had a nice little confusion

Answer 5

i said let u = x-1 but it got confusing to write it in terms of u.

Answer 6

does the identity tan(x) = sin(2x) / ( cos (2x) + 1) help ?

Answer 7

no. it makes it more tedious to do but good thinking

Answer 8

not sure. if you figure it out without L'Hopital let me know.

Answer 9

wait the top factors to \[(x-1)^{3}\]

so now i can write it as u= x-1

Answer 10

\[\lim_{u \to 0} \frac{u^{3}}{tanu - sinu}\]

Answer 11

it does. but how do you proceed?

Answer 12

are you allowed to use taylor expansions?