Find the limit.
$\(\lim\)_{x\(\rarr\)0}x^3+5x^2-7x+3$

5. Which of the following functions grow faster than ln(x) as x→∞? Which grow at the same rate as ln(x)? Which grow slower?

a. log_3(x)

5. Which of the following functions grow faster than ln(x) as x→∞? Which grow at the same rate as ln(x)? Which grow slower?

c. ln(√x)

11. Show that if positive functions f(x) and g(x) grow at the same rate as x→∞, then f=O(g) and g=O(f).

13. When is a polynomial f(x) of at most the order of a polynomial g(x) as x→∞? Give reasons for your answer.

Find the limit.

$\(\lim\)_{x\(\rarr\)2}\(\sqrt{x^2+5}\)$

Find the limit.

$\(\lim\)_{x\(\rarr\)3}\(\frac{x^2+2x-3}{x-2}\)$

Find the limit.

$\(\lim\)_{x\(\rarr\)0}\(\frac{3x^2+7x}{x}\)$

Find the limit.

$\(\lim\)_{x\(\rarr\)2}\(\frac{x^2-7x+12}{x-3}\)$