Question

Easy way to learn squeeze theorem???

Answer 1

Just think of the word "Squeeze" (btw what class is this for)?

Answer 2

College Calculus

Answer 3

if a<=b<=c and a = c, then a=b=c

think about this, if you are greater than or equal height to some person, lets call him john
and you are less than or equal height than some guy named jack, then
john<=you<=jack
now
if jack is the same height as john, you must be the same height as both of them

Answer 4

think about \(\lim_{x\rightarrow \infty}\frac{\sin(x)}{x}\)
\[-1\le\sin(x)\le1\]
now divide everything by x
\[\frac{-1}{x}\le\frac{\sin(x)}{x}\le\frac{1}{x}\]
so we know this
\[\lim_{n\rightarrow \infty}\frac{-1}{x}\le\lim_{n\rightarrow \infty}\frac{\sin(x)}{x}\le \lim_{n\rightarrow \infty}\frac{1}{x}\] now take the limit of the outside functions

so\[0\le\frac{\sin(x)}{x}\le0\]
so
\[\lim_{n\rightarrow \infty}\frac{\sin(x)}{x}=0\]

Answer 5

I know you could have found this limit with LaHopital's Rule, but it makes for a good example.

Answer 6

also note that when we divided by x, we did not have to change the inequality signs because we are considering x to be large, so we may assume its positive.

Answer 7

Thank you @zzr0ck3r !