Answer:
The value of given limit problem is 0.
Step-by-step explanation:
The given limit problem is
[tex]lim_{x\rightarrow \infty}\dfrac{6x^3+5x-7}{6x^4-4x^3-9}[/tex]
We need to find the value of given limit problem.
Divide the numerator and denominator by the leading term of the denominator, i.e., [tex]x^4[/tex]
[tex]lim_{x\rightarrow \infty}\dfrac{\frac{6x^3+5x-7}{x^4}}{\frac{6x^4-4x^3-9}{x^4}}[/tex]
[tex]lim_{x\rightarrow \infty}\dfrac{\frac{6}{x}+\frac{5}{x^3}-\frac{7}{x^4}}{6-\frac{4}{x}-\frac{9}{x^4}}[/tex]
Apply limit.
[tex]\dfrac{\frac{6}{ \infty}+\frac{5}{ \infty}-\frac{7}{ \infty}}{6-\frac{4}{ \infty}-\frac{9}{ \infty}}[/tex]
We know that [tex]\frac{1}{\infty}=0[/tex].
[tex]\dfrac{0+0-0}{6-0-0}[/tex]
[tex]\dfrac{0}{6}[/tex]
[tex]0[/tex]
Hence, the value of given limit is 0.
