When comparing 2 infinitesimals, does the higher order one approach 0 faster or slower?
I know how to do the maths, here I'm asking just about the statement.anuttarasammyak said:Why don't you take the ratio of the two to see it ?
how did you define speed/fastanuttarasammyak said:##x^3## goes to zero faster than ##x^2##, ##|x^3|<|x^2|##, when x of -1< x < 1 approaches to zero.
feynman1 said:how did you define speed/fast
Infinitesimals are mathematical objects that are infinitely small, but not equal to zero. They are used in calculus to represent quantities that approach zero, but never actually reach it.
Infinitesimals are used in calculus to represent rates of change, such as the slope of a curve or the velocity of an object. They allow us to analyze and solve problems involving continuously changing quantities.
Yes, infinitesimals can be both positive and negative. They are simply numbers that are infinitely close to zero, so they can take on any value on the number line.
No, infinitesimals and limits are not the same. Infinitesimals are used in non-standard analysis, while limits are used in standard analysis. Infinitesimals are also defined as actual numbers, while limits are a concept used to approach a value.
Infinitesimals are important in calculus because they allow us to analyze and understand continuously changing quantities. They also help us to solve complex problems in physics, engineering, and other fields that involve rates of change.