1. ## Limits Problem

Hi everyone this is what the problem asks:

Evaluate the Limit and Justify each step by indicating the appropriate Limit Law(s).

Lim
X→0 (cos4x)/( 5+2x3 )

2. Originally Posted by Asuhuman18
Hi everyone this is what the problem asks:

Evaluate the Limit and Justify each step by indicating the appropriate Limit Law(s).

Lim
X→0 (cos4x)/( 5+2x3 )

$\lim_{x \to 0}\frac{\cos{4x}}{5 + 2x^3}$.

If so, first note that the numerator and denominator are both continuous at $x = 0$, and the denominator does not $\to 0$.

These are the limit laws you will use...

1. If $f(x)$ is continuous at $x = a$, then $\lim_{x \to a}f(x) = f(a)$.

2. $\lim_{x \to a}\frac{f(x)}{g(x)} = \frac{\lim_{x \to a}f(x)}{\lim_{x \to a}g(x)}$ if $g(x)$ does not $\to 0$.

Thus

$\lim_{x \to 0}\frac{\cos{4x}}{5 + 2x^3} = \frac{\lim_{x \to 0}\cos{4x}}{\lim_{x \to 0}5 + 2x^3}$

$= \frac{\cos{4\cdot 0}}{5 + 2(0)^3}$

$= \frac{1}{5}$.

3. yeah thanks a lot man.