Question

find the limit of the rational function a. as x→∞ and b. as x→ - ∞. h(x)=\frac{18x^{4}}{15x^{4}+10x^{3}+2x^{2}} a. lim_{x \to infty}\frac{18x^{4}}{15x^{4}+10x^{3}+2x^{2}}=square (simplify your answer.)

Explanation:

Step1: Divide numerator and denominator by highest - power of x

Divide both the numerator and denominator of the function $\frac{18x^{4}}{15x^{4}+10x^{3}+2x^{2}}$ by $x^{4}$. We get $\lim_{x
ightarrow\infty}\frac{18x^{4}/x^{4}}{(15x^{4}+10x^{3}+2x^{2})/x^{4}}=\lim_{x
ightarrow\infty}\frac{18}{15 + 10/x+2/x^{2}}$.

Step2: Evaluate the limit

As $x
ightarrow\infty$, $\frac{10}{x}
ightarrow0$ and $\frac{2}{x^{2}}
ightarrow0$. So, $\lim_{x
ightarrow\infty}\frac{18}{15 + 10/x+2/x^{2}}=\frac{18}{15+0 + 0}$.

Step3: Simplify the result

$\frac{18}{15}=\frac{6}{5}$.

Answer:

$\frac{6}{5}$