- #1
kitle545
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Homework Statement
lim (SQRT (8x^3 + 5x + 10) ) / x^2
x -> infinity
Homework Equations
The Attempt at a Solution
I tried factoring out x^3, but that didn't help anything.
The concept of "limit approaching infinity" refers to the behavior of a function as its input approaches infinity. In other words, it describes what happens to the output of a function as its input gets larger and larger.
The key difference between "limit approaching infinity" and "limit at infinity" is that in the former, the input is getting closer and closer to infinity but never actually reaches it, while in the latter, the input is actually equal to infinity.
The limit as the input approaches infinity can either approach a finite value (e.g. a number like 5), approach infinity itself, or oscillate between different values. In some cases, the limit may not exist at all.
Examples of functions with limits approaching infinity include polynomial functions with a positive leading coefficient, exponential functions, and rational functions with a larger degree in the numerator than in the denominator.
"Limit approaching infinity" is a fundamental concept in calculus and is used in various fields such as physics, economics, and engineering. It can be used to model and analyze the behavior of systems as they approach extreme values, such as the growth of a population or the speed of an object as it approaches a barrier.