Find the limit or show that it does not exist. limx→∞=1−x2x3−x+1

Divide everything by the highes power of x, so x3 limx→∞1−x2x3−x+1=limx→∞1x3−1x1−1x2+1x3 Then as x→∞ terms 1x3,1x2,1x approach 0. 0−01−0+0=01=0 limx→∞1−x2x3−x+1=0

"Find the limit or show that it does..." solved and explained

elchatosarapage

Answered question

2021-11-11

Find the limit or show that it does not exist.

lim_{x \to \infty} = \frac{1 - x^{2}}{x^{3} - x + 1}

Answer & Explanation

Charles Clute

Beginner2021-11-12Added 17 answers

Divide everything by the highes power of x, so

x^{3}

lim_{x \to \infty} \frac{1 - x^{2}}{x^{3} - x + 1} = lim_{x \to \infty} \frac{\frac{1}{x^{3}} - \frac{1}{x}}{1 - \frac{1}{x^{2}} + \frac{1}{x^{3}}}

Then as

x \to \infty

terms

\frac{1}{x^{3}}, \frac{1}{x^{2}}, \frac{1}{x}

approach 0.

\frac{0 - 0}{1 - 0 + 0} = \frac{0}{1} = 0

lim_{x \to \infty} \frac{1 - x^{2}}{x^{3} - x + 1} = 0

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