Mirza Aslam Beig

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Find the given limit. $$ \lim _{x \rightarrow \infty} 4 /(2-x) $$

   Find the given limit.
$$
\lim _{x \rightarrow \infty} 4 /(2-x)
$$

Calculus with Concepts in Calculus

Calculus with Concepts in Calculus

Denny Gulick, Robert… 6th Edition

Chapter 4, Problem 2

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Solved by Expert Mirza Aslam Beig

04/11/2022

Step 1

$$ \lim _{x \rightarrow \infty} \frac{4}{2-x} = \frac{4}{2-\infty} $$ Show more…

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Find the given limit. $$ \lim _{x \rightarrow \infty} 4 /(2-x) $$

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Key Concepts

Limits at Infinity

This concept involves studying the behavior of a function as its variable approaches infinity. It helps determine the end behavior of functions by considering how different parts of the function contribute to its value when the variable becomes very large.

Rational Functions

Rational functions are expressions formed by the ratio of two polynomials. Analyzing their limits, especially as the variable tends to infinity, often involves comparing the degrees of the polynomials in the numerator and denominator to understand the function's asymptotic behavior.

Dominant Term Analysis

In the analysis of limits, especially for rational functions, the dominant term is the part of the expression that grows fastest as the variable increases. By focusing on these terms, one can simplify the evaluation of the limit by neglecting terms that have a relatively insignificant impact on the behavior of the function as the variable approaches infinity.

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