Question

HELPP! Brainliest is rewarded!

Answer 1

Answer:

DNE (does not exist)

Step-by-step explanation:

Our function is: $f(x)=\frac{x^2+2x}{x^4}$. We want to find the limit of this as x approaches 0. The first thing we would want to do is to substitute 0 in for x. But when we do that, we get 0/0, which is undefined:

$\frac{0^2+2*0}{0^4}=\frac{0}{0}$

Let's divide the numerator and denominator both by x:

$\frac{x^2+2x}{x^4}=\frac{x+2}{x^3}$

Now substitute 0 in again:

$\frac{0+2}{0^3}=\frac{2}{0}$

Because we have a number divided by 0, this cannot exist. If we graph this function (see attachment), we'll also see that the graph diverges at x = 0, so the limit does not exist.

Answer 2

Answer:

Limit doesn't exist

Step-by-step explanation:

As x --> 0,

(x² + 2x)/x⁴

From the LHS:

Let x = -0.1, (x² + 2x)/x⁴ = -1900

From the RHS:

Let x = 0.1, (x² + 2x)/x⁴ = 2100

Therefore the limit doesn't exist