Math Snap

STEP 1

Assumptions1. We are asked to find the limit as x approaches infinity for the function $\frac{4x-1}{x+1}$.
. We are given that the limit equals.

STEP 2

We start by writing down the given limit expression.
$$\lim{x \rightarrow+\infty} \frac{4 x-1}{2 x+1}$$

STEP 3

We divide the numerator and the denominator by $x$, which is the highest power of $x$ in the denominator.
$$\lim{x \rightarrow+\infty} \frac{\frac{x}{x}-\frac{1}{x}}{\frac{2x}{x}+\frac{1}{x}}$$

STEP 4

implify the expression.
$$\lim{x \rightarrow+\infty} \frac{4-\frac{1}{x}}{2+\frac{1}{x}}$$

STEP 5

As $x$ approaches infinity, $\frac{1}{x}$ approaches0. So, we can replace $\frac{1}{x}$ with0 in the expression.
$$\lim{x \rightarrow+\infty} \frac{4-0}{2+0}$$

implify the expression to find the limit.
$$\lim{x \rightarrow+\infty} \frac{4}{2} =2$$The limit of the function as $x$ approaches infinity is indeed2.