# How do you solve this problem? Please explain step by step.

## find lim x--->0 3x^3+25x/x^2+5x

Sep 19, 2017

5

#### Explanation:

I thought the expression for F might have a typo, and that both first and second term were divided by the sum of the third and fourth term.

Here is the strategy. All positive powers of x will tend to zero as x approaches zero. All negative powers will approach infinity.
Let's call F the fraction.
If
$F = \setminus \frac{3 {x}^{3} + 25 x}{{x}^{2} + 5 x}$

$F = \setminus \frac{3 {x}^{2} + 25}{x + 5}$

In the numerator, $25 + 3 {x}^{2} \setminus \to 25 + 3 \left(0\right) = 25$ when $x \setminus \to 0$. Likewise $x + 5 \setminus \to 0 + 5$ when $x \setminus \to 0$. Their ratio tends to $\frac{25}{5} = 5$.

If F has the expression you wrote, then

$F = 3 {x}^{3} + \frac{25}{x} + 5 x$, which tends to infinity as x approaches zero.