Question

what happens to the value of the function y = \frac{190x}{2x - 1} as x approaches infinity?
a. y approaches 0
b. y approaches 1
c. y approaches 95
d. y approaches 190
e. y approaches infinity

Explanation:

Step1: Divide numerator and denominator by x

Divide both the numerator $190x$ and the denominator $2x - 1$ of the function $y=\frac{190x}{2x - 1}$ by $x$. We get $y=\frac{190}{\ 2-\frac{1}{x}}$.

Step2: Evaluate the limit as x approaches infinity

As $x
ightarrow\infty$, $\frac{1}{x}
ightarrow0$. So, $\lim_{x
ightarrow\infty}y=\lim_{x
ightarrow\infty}\frac{190}{2-\frac{1}{x}}=\frac{190}{2 - 0}$.

Step3: Calculate the final value

$\frac{190}{2-0}=\frac{190}{2}=95$.

Answer:

C. y approaches 95