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Why is the function ex the natural number e raised to the power of x so special from the calculus point of view?
Wiki User
∙ 10y ago
That's because powers that involve the power "e", and logarithms to the base "e", are simpler than other powers or logarithms. For example: the derivative of ex is ex, while a derivative with other bases is more complicated; while the derivative of the natural logarithm (ln x, or logex) is 1/x.
Wiki User
∙ 10y ago
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Which is bigger real numbers or natural numbers?
Natural number are a special kind of real number. They both are large without bounds. For every real number there is a larger natural number and for every natural number there is a larger real number.
How is number 1 special?
It is the only Natural which is neither Prime nor Composite.
Why radioactivity is exponential?
The number of atoms that decay in a certain time is proportional to the amount of substance left. This naturally leads to the exponential function. The mathematical explanation - one that requires some basic calculus - is that the only function that is its own derivative (or proportional to its derivative) is the exponential function (or a slight variation of the exponential function).
What is the difference between a logarithmic function and a natural logarithmic function?
Ans: A natural log function ALWAYS has base e ( e is the irrational number that is the sum of the infinite series 2 + 1 / 2! + 1 /3! + 1 /4! + . . . )
What is the name to substitute a number or expression into a function?
Substituting a name is "evaluating". But there is no special name for substituting an expression.
Application of integral calculus on food?
There is an HUGE number of applications but I'll give you an example: Say you have a function of food consumption (independent variable) against number of people. If you integrate this function you will get a figure for total food consumption.
Is sequence a function?
yes it is a function because sequence defined as "a function whose domain is set of natural number"
Which is bigger real numbers or natural numbers?
Natural number are a special kind of real number. They both are large without bounds. For every real number there is a larger natural number and for every natural number there is a larger real number.
A sequence is a whose domain is the set of natural number?
A sequence is a function ! whose domian is the set of natural numbers
Limits in calculus?
A limit in calculus is a value which a function, f(x), approaches at particular value of x. They can be used to find asymptotes, or boundaries, of a function or to find where a graph is going in ambiguous areas such as asymptotes, discontinuities, or at infinity. There are many different ways to find a limit, all depending on the particular function. If the function exists and is continuous at the value of x, then the corresponding y value, or f (x), is the limit at that value of x. However, if the function does not exist at that value of x, as happens in some trigonometric and rational functions, a number of calculus "tricks" can be applied: such as L'Hopital's Rule or cancelling out a common factor.
How is number 1 special?
It is the only Natural which is neither Prime nor Composite.
Why radioactivity is exponential?
The number of atoms that decay in a certain time is proportional to the amount of substance left. This naturally leads to the exponential function. The mathematical explanation - one that requires some basic calculus - is that the only function that is its own derivative (or proportional to its derivative) is the exponential function (or a slight variation of the exponential function).
What is the difference between a logarithmic function and a natural logarithmic function?
Ans: A natural log function ALWAYS has base e ( e is the irrational number that is the sum of the infinite series 2 + 1 / 2! + 1 /3! + 1 /4! + . . . )
What is limits in calculus?
limits in calculus is when x approaches specific number such as x approaches 2 x is approximately 2
What is the standard log base at plus 2 level?
What is a standard log? log on calculator is based 10, and ln is based e. e is a VERY special number, and you will know why in Calculus.
What is the name to substitute a number or expression into a function?
Substituting a name is "evaluating". But there is no special name for substituting an expression.
What is so special about number 1?
1 is the smallest natural number. 1 is the factor of every number. 1 is neither prime nor composite.
