Typo?lukatwo said:Homework Statement
I've read in my textbook, and confirmed via WolframAlpha that lim n->0 (cosx/x^0) =1
lukatwo said:, and need an explanation for it. I thought it should be ∞.
Homework Equations
The Attempt at a Solution
I tried to use L'Hospitale on the expression, but that led to nowhere. There's no intermediate step between the expression and solution in both textbook, and Wolfram.
Yes to both questions. The graph of y = x0 is a horizontal line with a hole at (0, 1).lukatwo said:From all this my guess will be 1, but still not clear why. Is it because lim x->0 means that x !=0 but rather close to 0? Meaning some infinitesimal number ^0=1? Am i getting that correctly?
A finite limit is the value that a function approaches as the input approaches a specific value or value range.
This is due to the fact that as x approaches 0, the value of cosx also approaches 1. Additionally, any non-zero number raised to the power of 0 is equal to 1.
The finite limit of cosx/x^0 helps us to understand the behavior of the function as the input approaches 0. It tells us that the function approaches a specific value, in this case 1, when x is close to 0.
The finite limit is the value that the function approaches as the input approaches a specific value or value range. On the other hand, the limit at a specific point is the value that the function approaches when the input approaches a specific value from both sides. The finite limit only considers the behavior of the function near the specific value, while the limit at a specific point considers the behavior of the function at the specific value itself.
Understanding the finite limit of cosx/x^0 is important in fields such as physics, engineering, and economics, where functions are used to model real-world phenomena. It can help in predicting the behavior of systems near critical points or thresholds. For example, in physics, it can be used to predict the behavior of an object as it approaches a barrier or threshold. In economics, it can be used to predict the behavior of a market as it approaches a critical point.