0
What else can I help you with?
What is Osborn's rule?
It is used in hyperbolic functions; it's the rule to change a normal trig function into hyperbolic trig function. Example: cos(x-y) = cosx cosy + sinx siny Cosh(x-y) = coshx coshy - sinhx sinhy Whenever you have a multiplication of sin, you write the hyperbolic version as sinh but change the sign. also applied when: tanxsinx (sinx)^2 etc... Hope this helps you
When you say a function is not differentiable?
Well, firstly, the derivative of a function simply refers to slope. Usually we say that the function is not differentiable at a point.Say you have a function such as this:f(x)=|x|Another way to represent that would be as a piece-wise function:g(x) = { -x for x= 0The problem arises at the specific point x=0. If you look at the slope--the change in the function--from the left and right of x, you notice that it is different, negative 1 and positive 1. So, we can say that the function is not differentiable at x=0 because of that sudden change.There are however, a few functions that are nowhere differentiable. One example is the Weirstrass function. The even more ironic thing about this function is that it is continuous everywhere! Since this function is not differentiable anywhere, many might call it a non-differentiable function.There are absolutely other examples.
How do you find inverse function?
If its a fraction then we can change the numerators and denominators upside down .This is in case of fraction.
What is the difference between a reciprocal function and an inverse function?
A reciprocal function will flip the original function (reciprocal of 3/5 is 5/3). An inverse function will change the x's and y's of the original function (the inverse of x<4,y>8 is y<4, x>8). Whenever a function is reflected over the line y=x, the result is the inverse of that function. The y=x line starts at the origin (0,0) and has a positive slope of one. All an inverse does is flip the domain and range.
What term describes a function in which there is a common difference between each y-vaule?
The term that describes a function with a common difference between each y-value is a "linear function." In a linear function, the relationship between the x-values and y-values can be represented by a straight line, and the constant difference between consecutive y-values indicates a constant rate of change, or slope. This is typically expressed in the form (y = mx + b), where (m) is the slope.
How do the average rates of change for a linear function differ from the average rates of change for an exponential function?
The average rate of change for a linear function is constant, meaning it remains the same regardless of the interval chosen; this is due to the linear nature of the function, represented by a straight line. In contrast, the average rate of change for an exponential function varies depending on the interval, as exponential functions grow at an increasing rate. This results in a change that accelerates over time, leading to greater differences in outputs as the input increases. Thus, while linear functions exhibit uniformity, exponential functions demonstrate dynamic growth.
What is the relationship between sound intensity and the decibel scale in terms of the exponential function?
The relationship between sound intensity and the decibel scale is logarithmic, not exponential. The decibel scale measures sound intensity in a way that reflects the human perception of sound, which is why it is logarithmic. This means that a small change in sound intensity corresponds to a larger change in decibels.
What are categories of function?
Categories of function can be broadly classified into several types, including linear functions, quadratic functions, polynomial functions, exponential functions, logarithmic functions, and trigonometric functions. Each category is defined by its unique mathematical properties and behavior. For instance, linear functions represent a constant rate of change, while quadratic functions exhibit a parabolic shape. These categories help in understanding and analyzing various mathematical models and real-world phenomena.
What is the most basic function in a family of functions?
The most basic function in a family of functions is typically considered to be the linear function, represented as ( f(x) = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. Linear functions serve as the foundation for understanding more complex functions, such as polynomial, exponential, and logarithmic functions. They exhibit a constant rate of change and are characterized by their straight-line graphs. This simplicity allows them to model a variety of real-world relationships.
How do you determine a function is linear or exponential?
To determine if a function is linear or exponential, examine its formula or the relationship between its variables. A linear function can be expressed in the form (y = mx + b), where (m) and (b) are constants, resulting in a constant rate of change. In contrast, an exponential function has the form (y = ab^x), with a variable exponent, indicating that the rate of change increases or decreases multiplicatively. Additionally, plotting the data can help; linear functions produce straight lines, while exponential functions create curves.
How do we change from logarithmic form to exponential form?
Logb (x)=y is called the logarithmic form where logb means log with base b So to put this in exponential form we let b be the base and y the exponent by=x Here is an example log2 8=3 since 23 =8. In this case the term on the left is the logarithmic form while the one of the right is the exponential form.
How do linear and exponential functions change over equal intervals?
The linear function changes by an amount which is directly proportional to the size of the interval. The exponential changes by an amount which is proportional to the area underneath the curve. In the latter case, the change is approximately equal to the size of the interval multiplied by the average value of the function over the interval.
What is exponential function?
"The" exponential function is ex. A more general exponential function is any function of the form AeBx, for any non-xero constants "A" and "B". Alternately, Any function of the form CDx (for constants "C" and "D") would also be considered an exponential function. You can change from one form to the other.
When would you use a power function and when would you use a exponential function?
Both of these functions are found to represent physical events in nature. A common form of the power function would be the parabola (power of 2). One example would be calculating distance traveled of an object with constant acceleration. d = V0*t + (a/2)*t². The exponential function describes many things, such as exponential decay: like the voltage change in a capacitor & radioactive element decay. Also exponential growth (such as compound interest growth).
What are exponential functions?
With exponentiation functions, the rate of change of the function is proportional to it present value.A function f(x) = ax is an exponentiation function [a is a constant with respect to x]Two common exponentiation functions are 10x and ex. The number 'e' is a special number, where the rate of change is equal to the value (not just proportional). When the number e is used, then it is called the exponential function.See related links.
What tables represent an exponential function. Find the average rate of change for the interval from x 7 to x 8.?
what exponential function is the average rate of change for the interval from x = 7 to x = 8.
Which exponential equation is equivalent to the logarithmic equation log 200 equals a?
Log 200=a can be converted to an exponential equation if we know the base of the log. Let's assume it is 10 and you can change the answer accordingly if it is something else. 10^a=200 would be the exponential equation. For a base b, we would have b^a=200
