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thharrimw
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do Logarithms play any major part in being able to do calculus?
mgb_phys said:More the other way around - the definition of ln() and 'e' are based on calculus.
mgb_phys said:The definition of ln(a) is the integral of 1/x from 0 to 'a'
mgb_phys said:The definition of ln(a) is the integral of 1/x from 0 to 'a'
is e a ratio?mgb_phys said:Try it! Just put in the first few terms.
To answer your original question, 'e' comes up in a few standard calculus solutuions.
And obviously knowing the rules about multiplying and adding exponents comes into a lot of calculus.
Not until you tell us what n is! Yes, for very large n, e is approximately that.thharrimw said:ok so the number e [tex]\approx[/tex] (1+1/n)^n
Not unless he/she were speaking very loosely. 'n' is never infinite. What is strictly true is that [itex]e= \lim_{n\rightarrow \infty}(1+ 1/n)^n[/itex].mgb_phys said:I suppose a mathematician would say that e was exactly (1+/1n)^n for infiinite 'n'
A logarithm is an inverse function to an exponential function. It is used to solve exponential equations and is commonly represented as log_{b}(x), where b is the base and x is the value.
Logarithms are used in calculus to simplify complex mathematical expressions involving exponents. They are also used to solve equations involving exponential growth and decay, which are important concepts in calculus.
Yes, calculus can be done without using logarithms. However, logarithms do play a major role in simplifying and solving equations, making the process more efficient and easier to understand.
The relationship between logarithms and exponential functions in calculus is that they are inverse functions of each other. This means that the logarithm of a number is the exponent needed to raise the base to get that number.
Yes, logarithms are used in many other areas of mathematics, such as statistics, finance, and physics. They are also commonly used in computer science and engineering to solve complex equations and algorithms.