Evaluate the limit

$\underset{x\to \mathrm{\infty}}{lim}\frac{4{x}^{3}-2}{3{x}^{4}+5x}$

arenceabigns
2020-12-02
Answered

Evaluate the limit

$\underset{x\to \mathrm{\infty}}{lim}\frac{4{x}^{3}-2}{3{x}^{4}+5x}$

You can still ask an expert for help

tafzijdeq

Answered 2020-12-03
Author has **92** answers

Given:

$\underset{x\to \mathrm{\infty}}{lim}\frac{4{x}^{3}-2}{3{x}^{4}+5x}$

To find:

The limit.$\underset{x\to \mathrm{\infty}}{lim}\frac{4{x}^{3}-2}{3{x}^{4}+5x}$

Solve:

$\underset{x\to \mathrm{\infty}}{lim}\frac{4{x}^{3}-2}{3{x}^{4}+5x}$

On multiplying and dividing by${x}^{4}$

$\underset{x\to \mathrm{\infty}}{lim}\frac{4{x}^{3}-2}{3{x}^{4}+5x}=\underset{x\to \mathrm{\infty}}{lim}\frac{{x}^{4}(\frac{4}{x}-\frac{2}{{x}^{4}})}{{x}^{4}(3-\frac{5}{{x}^{3}})}$

On cancelling the common term,

$\underset{x\to \mathrm{\infty}}{lim}\frac{4{x}^{3}-2}{3{x}^{4}+5x}=\underset{x\to \mathrm{\infty}}{lim}\frac{(\frac{4}{x}-\frac{2}{{x}^{4}})}{(3-\frac{5}{{x}^{3}})}$

Substitute the variable with value,

$\underset{x\to \mathrm{\infty}}{lim}\frac{4{x}^{3}-2}{3{x}^{4}+5x}=\underset{x\to \mathrm{\infty}}{lim}\frac{(4(0)-2(0))}{(3-5(0))}$

$\underset{x\to \mathrm{\infty}}{lim}\frac{4{x}^{3}-2}{3{x}^{4}+5x}=0$

To find:

The limit.

Solve:

On multiplying and dividing by

On cancelling the common term,

Substitute the variable with value,

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