Operations with infinity Calculator

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Example

Created on 2024-06-20Asked by Scarlett Jones (Solvelet student)

Evaluate the limit

\lim_{x \to \infty} \frac{5x^2 - 3x + 2}{2x^2 + 7x + 1}

Solution

To evaluate the limit

\lim_{x \to \infty} \frac{5x^2 - 3x + 2}{2x^2 + 7x + 1}

, follow these steps: 1. Divide the numerator and the denominator by

x^2

\lim_{x \to \infty} \frac{5 - \frac{3}{x} + \frac{2}{x^2}}{2 + \frac{7}{x} + \frac{1}{x^2}}.

2. As

x \to \infty

, the terms

\frac{3}{x}

\frac{2}{x^2}

\frac{7}{x}

, and

\frac{1}{x^2}

approach 0:

\lim_{x \to \infty} \frac{5 - 0 + 0}{2 + 0 + 0} = \frac{5}{2}.

Therefore, the limit is

\frac{5}{2}

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Eleanor Hernandez on Solvelet

1. Evaluate the limit

\lim_{{x \to \infty}} (3x^2 + 4x - 2)

.2. Determine whether the limit

\lim_{x \rightarrow -\infty} \frac{1}{x}

exists.

DefinitionOperations with infinity Generalize rules of limits and arithmetic to working with infinity, an abstract concept which has no natural rules as in ordinary arithmetic and algebra. Infinity (∞) is actually not a number, it is a symbol that denotes a limitless quantity. The basic rules are that =∞+∞ is ∞, ∞−∞ is in the form of x which is indeterminate, ∞⋅∞=∞, and ∞1=0. Examples: Limits: The limit x→∞x1=0,

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