Question

Evaluate the limit lim_{xrightarrowinfty}frac{4x^3-2}{3x^4+5x}

Limits and continuity
ANSWERED
asked 2020-12-02
Evaluate the limit
\(\lim_{x\rightarrow\infty}\frac{4x^3-2}{3x^4+5x}\)

Answers (1)

2020-12-03
Given:
\(\lim_{x\rightarrow\infty}\frac{4x^3-2}{3x^4+5x}\)
To find:
The limit. \(\lim_{x\rightarrow\infty}\frac{4x^3-2}{3x^4+5x}\)
Solve:
\(\lim_{x\rightarrow\infty}\frac{4x^3-2}{3x^4+5x}\)
On multiplying and dividing by \(x^4\)
\(\lim_{x\rightarrow\infty}\frac{4x^3-2}{3x^4+5x}=\lim_{x\rightarrow\infty}\frac{x^4(\frac{4}{x}-\frac{2}{x^4})}{x^4(3-\frac{5}{x^3})}\)
On cancelling the common term,
\(\lim_{x\rightarrow\infty}\frac{4x^3-2}{3x^4+5x}=\lim_{x\rightarrow\infty}\frac{(\frac{4}{x}-\frac{2}{x^4})}{(3-\frac{5}{x^3})}\)
Substitute the variable with value,
\(\lim_{x\rightarrow\infty}\frac{4x^3-2}{3x^4+5x}=\lim_{x\rightarrow\infty}\frac{(4(0)-2(0))}{(3-5(0))}\)
\(\lim_{x\rightarrow\infty}\frac{4x^3-2}{3x^4+5x}=0\)
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