Question

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

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

Answer 1

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 = \frac{3 x^3 + 25x}{x^2 + 5x}`

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

In the numerator, `25 + 3x^2 \to 25 + 3(0) = 25` when `x\to 0`. Likewise `x + 5\to 0 + 5` when `x \to 0`. Their ratio tends to `25/5 = 5`.

If F has the expression you wrote, then

`F = 3 x^3 + 25/x + 5x`, which tends to infinity as x approaches zero.