Question

Find the limit as h approaches 0, lim h/sin3h?

Answer 1

Recall
\[\lim_{u \rightarrow 0}\frac{u}{\sin(u)}=1\]
By squeeze thm.

Answer 2

\[\lim_{h \rightarrow 0}\frac{h}{\sin(3h)}=\lim_{h \rightarrow 0}\frac{a}{a} \frac{h}{\sin(3h)}\]
\[\lim_{h \rightarrow 0}\frac{1}{a} \frac{ah}{\sin(3h)}=\frac{1}{a}\lim_{h \rightarrow 0}\frac{ah}{\sin(3h)}\]
\[=\frac{1}{a}(1)=\frac{1}{a}\]

what does a need to be in order for this to be true?

Answer 3

a needs a 3

Answer 4

Right on! :)

Answer 5

\[\lim_{h \rightarrow 0}\frac{ah}{\sin(ah)}=1 , a \neq 0\]

Answer 6

I hope this was helpful. Do you have any questions?

Answer 7

yes that was very helpful, would you know how to graph f(x) (1-x2, x doesn't equal 1)
(2, x=1)

Answer 8

Ok so do you know how to just graph y=1-x^2 ?

Answer 9

yes