There are no points of discontinuity for exponential functions since the domain of the general exponential function consists of all real values!
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
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.
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,
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,
Yes.
chicken
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.
neither linear nor exponential functions have stationary points, meaning their gradients are either always +ve or -ve
They have infinite domains and are monotonic.
They are inverses of each other.
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.