He memorized tables of functions, exponential functions, logarithmic functions, etc, ... try looking up "handbook of mathematical functions"
exponent of any number is more than 0
If the common ratio is negative then the points are alternately positive and negative. While their absolute values will lie on an exponential curve, an oscillating sequence will not lie on such a curve,
There are lots of situations that are not modelled by exponential functions. A simple example is when something increases linearly. For example, assuming you have a fixed daily income, and save all of it, the amount of money you have is directly proportional to the number of days worked. No exponential function there, whatsoever.There are lots of situations that are not modelled by exponential functions. A simple example is when something increases linearly. For example, assuming you have a fixed daily income, and save all of it, the amount of money you have is directly proportional to the number of days worked. No exponential function there, whatsoever.There are lots of situations that are not modelled by exponential functions. A simple example is when something increases linearly. For example, assuming you have a fixed daily income, and save all of it, the amount of money you have is directly proportional to the number of days worked. No exponential function there, whatsoever.There are lots of situations that are not modelled by exponential functions. A simple example is when something increases linearly. For example, assuming you have a fixed daily income, and save all of it, the amount of money you have is directly proportional to the number of days worked. No exponential function there, whatsoever.
A vertical asymptote can be, but need not be a discontinuity. In simple terms, the distinction depends whether the domain extends on only one side of the (no discontinuity) or both sides (infinite discontinuity). For example, there is no discontinuity in f(x) = 1/x for x > 0 On the other hand, f(x) = 1/x for x ≠0 has an infinite discontinuity at x = 0.
Exponential and logarithmic functions are inverses of each other.
Polynomials are continuous everywhere, so there are not points of discontinuity.
Exponential and logarithmic functions are different in so far as each is interchangeable with the other depending on how the numbers in a problem are expressed. It is simple to translate exponential equations into logarithmic functions with the aid of certain principles.
Do you mean "equations involving exponential functions"? Yes,
Power functions are functions of the form f(x) = ax^n, where a and n are constants and n is a real number. Exponential functions are functions of the form f(x) = a^x, where a is a constant and x is a real number. The key difference is that in power functions, the variable x is raised to a constant exponent, while in exponential functions, a constant base is raised to the variable x. Additionally, exponential functions grow at a faster rate compared to power functions as x increases.
Yes.
chicken
neither linear nor exponential functions have stationary points, meaning their gradients are either always +ve or -ve
Trigonometric functions, exponential functions are two common examples.
The exponential function, logarithms or trigonometric functions are functions whereas a complex variable is an element of the complex field. Each one of the functions can be defined for a complex variable.
There are several laws of exponential functions, not just one. Here is just one of them:The derivative of THE exponential function (base e) is the same as the function itself.
They have infinite domains and are monotonic.