Question

Use the properties of limits to help decide whether the limit exists. If the limit​ exists, find its value. ModifyingBelow lim With x right arrow infinity StartFraction 6 x cubed plus 5 x minus 7 Over 6 x Superscript 4 Baseline minus 4 x cubed minus 9 EndFraction

Answer 1

Answer:

The value of given limit problem is 0.

Step-by-step explanation:

The given limit problem is

$lim_{x\rightarrow \infty}\dfrac{6x^3+5x-7}{6x^4-4x^3-9}$

We need to find the value of given limit problem.

Divide the numerator and denominator by the leading term of the denominator, i.e., $x^4$

$lim_{x\rightarrow \infty}\dfrac{\frac{6x^3+5x-7}{x^4}}{\frac{6x^4-4x^3-9}{x^4}}$

$lim_{x\rightarrow \infty}\dfrac{\frac{6}{x}+\frac{5}{x^3}-\frac{7}{x^4}}{6-\frac{4}{x}-\frac{9}{x^4}}$

Apply limit.

$\dfrac{\frac{6}{ \infty}+\frac{5}{ \infty}-\frac{7}{ \infty}}{6-\frac{4}{ \infty}-\frac{9}{ \infty}}$

We know that $\frac{1}{\infty}=0$.

$\dfrac{0+0-0}{6-0-0}$

$\dfrac{0}{6}$

$0$

Hence, the value of given limit is 0.