Question

evaluate:
trig limit

Answer 1

\[\lim_{x \rightarrow 0} \frac{ xtanx^3 }{ x^4}\]

Answer 2

what is being cubed? just the \(x\) i take it

Answer 3

just the x

Answer 4

first cancel an \(x\) top and bottom and get
\[\frac{\tan(x^3)}{x^3}\]

Answer 5

then rewrite it as
\[\frac{\sin(x^3)}{x^3}\times \frac{1}{\cos(x^3)}\]

Answer 6

now it should be more or less obvious

Answer 7

sorry… i lied.. he has the question written down worn on my assignment.. the tanx is cubed

Answer 8

ok no matter, it is still 1

Answer 9

you have 3 copies of \(\frac{\sin(x)}{x}\) and one \(\frac{1}{\cos^3(x)}\)

Answer 10

\(\cos(0)=1\) and \(\lim_{x\to 0}\frac{\sin(x)}{x}=1\)

Answer 11

oh that's a lot simpler than i thought…. thanks!!!