Limits to infinity Calculator

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Example

Created on 2024-06-20Asked by Daniel Baker (Solvelet student)

Find the limit

\lim_{x \to \infty} \frac{3x^2 + 2x + 1}{2x^2 - x + 4}

Solution

To find the limit

\lim_{x \to \infty} \frac{3x^2 + 2x + 1}{2x^2 - x + 4}

, we divide the numerator and the denominator by the highest power of

x

in the denominator, which is

x^2

\lim_{x \to \infty} \frac{3x^2 + 2x + 1}{2x^2 - x + 4} = \lim_{x \to \infty} \frac{3 + \frac{2}{x} + \frac{1}{x^2}}{2 - \frac{1}{x} + \frac{4}{x^2}}

x \to \infty

, the terms

\frac{2}{x}

\frac{1}{x^2}

\frac{1}{x}

, and

\frac{4}{x^2}

all approach 0. Therefore, the limit simplifies to:

\frac{3 + 0 + 0}{2 - 0 + 0} = \frac{3}{2}

Thus:

\lim_{x \to \infty} \frac{3x^2 + 2x + 1}{2x^2 - x + 4} = \frac{3}{2}

Solved on Solvelet with Basic AI Model

Some of the related questions asked by Michael King on Solvelet

1. Find the limit

\lim_{{x \to \infty}} \frac{{1}}{{x}}

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

DefinitionAn infinite limit defines the function as the input approaches infinity. Tool to understand end behavior and asymptote behavior of functions. Example: lim⁡x→∞x1=0; as x gets large, x1 is close to zero.

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