Limits help: tan pix / x, x^2 sin(1/x), x csc x

[Ummy]

I don't remember A LOT about limits with trig. functions. We're reviewing and I'm having so much trouble.

We haven't done L'Hopital's rule, so please don't suggest it. People have tried to help me solve it this way but I just cannot understand it. There needs to be another way to solve these limits.

Please, please help me out?

There are questions like:

Lim x-->0 (tan ?x/ x)
Lim x---> infinity (x^2 sin(1/x)
lim x--> 0 (x csc x)

Do I use the quotient rule? Or...? I'm so confused!

Please help me. My HW is due tomorrow and I'm desperate for help!

Thank you SO much!

 

[Deleted member 4993]

Re: Limits help...:[

I don't remember A LOT about limits with trig. functions. We're reviewing and I'm having so much trouble.

We haven't done L'Hopital's rule, so please don't suggest it. People have tried to help me solve it this way but I just cannot understand it. There needs to be another way to solve these limits.

Please, please help me out?

There are questions like:

Lim x-->0 (tan ?x/ x)
Lim x---> infinity (x^2 sin(1/x)
lim x--> 0 (x csc x)

Do I use the quotient rule? Or...? I'm so confused!

Please help me. My HW is due tomorrow and I'm desperate for help!

Thank you SO much!

In all the above problems you need to use:

lim[x -> 0] {sin(x)/x} = 1

and/or

lim[x -> 0] {tan(x)/x} = 1

for example in problem #1

replace

[pi] x = u

then you need to find limit of

lim [u -> 0] {tan(u)/(u/[pi])} .... and continue.

 

[galactus]

Re: Limits help...:[

This one is similar to the famous sin(x)/x=1 limit.

\(\displaystyle \lim_{x\to\0}xcsc(x)=\lim_{x\to\0}\frac{x}{sin(x)}=1\)