1. ## Evaluate Limits help

I give up on these three How do you evaluate these using limit properties :*( Help?

(1) lim x-->0 sin 3x / x + x^2 + x^3

(2)lim x-->3 sqrt x^2 + 7 − sqrt x + 13 / sqrt x^3 − 2 − sqrt 2x + 19 (each sqrt covers the entire poly)

(3)lim x-->+infiniti 2x^2 + |x| cosx/ 3x^2 + 5

2. #1

Expand

$\displaystyle \lim_{x \rightarrow\ 0} \frac{sin(3x) + x^3 + x^4}{x}$

If you plugh in 0 for x, you get 0/0.

Use L'Hopital's rule.

3. Originally Posted by alexsmith2139
I give up on these three How do you evaluate these using limit properties :*( Help?

(1) lim x-->0 sin 3x / x + x^2 + x^3

(2)lim x-->3 sqrt x^2 + 7 − sqrt x + 13 / sqrt x^3 − 2 − sqrt 2x + 19 (each sqrt covers the entire poly)

(3)lim x-->+infiniti 2x^2 + |x| cosx/ 3x^2 + 5
Specify them.
The first one is $\displaystyle \frac{sin(3x)}{x+x^2+x^3}$ or $\displaystyle \frac{sin(3x)}{x}+x^2+x^3$ ??!
Use brackets to make them readable.

4. ^Yes, General is right. The first one I "assumed" that it was (sin(3x))/x without any other denominators.