find the limit of the rational function a. as ( x\rightarrowinfty ) and b. as ( x\rightarrow-infty ). write…

find the limit of the rational function a. as ( x\rightarrowinfty ) and b. as ( x\rightarrow-infty ). write ( infty ) or ( -infty ) where appro\n\n( f(x)=\frac{x + 3}{x^{2}+18} )\n\na. ( lim_{x\rightarrowinfty}\frac{x + 3}{x^{2}+18}=square ) simplify your answer.)

find the limit of the rational function a. as ( x\rightarrowinfty ) and b. as ( x\rightarrow-infty ). write ( infty ) or ( -infty ) where appro\n\n( f(x)=\frac{x + 3}{x^{2}+18} )\n\na. ( lim_{x\rightarrowinfty}\frac{x + 3}{x^{2}+18}=square ) simplify your answer.)

Answer

Explanation:

Step1: Divide numerator and denominator by (x^{2})

$$\lim_{x\rightarrow\infty}\frac{x + 3}{x^{2}+18}=\lim_{x\rightarrow\infty}\frac{\frac{x}{x^{2}}+\frac{3}{x^{2}}}{\frac{x^{2}}{x^{2}}+\frac{18}{x^{2}}}$$

Step2: Simplify the expression

$$=\lim_{x\rightarrow\infty}\frac{\frac{1}{x}+\frac{3}{x^{2}}}{1 + \frac{18}{x^{2}}}$$

Step3: Apply the limit

As (x\rightarrow\infty), (\lim_{x\rightarrow\infty}\frac{1}{x}=0) and (\lim_{x\rightarrow\infty}\frac{1}{x^{2}} = 0). $$=\frac{0 + 0}{1+0}$$

Answer:

(0)