Class 12

The average rate of change is meant to be a representation of the total change in one variable in comparison to the total change in another variable. This comparison is made between the two variables. The method of determining the exact rate of change of one variable in relation to an exact, infinitesimally minute change […]

What to do after 10th? The rate of change of a function to a variable is called the derivative in mathematics. To answer issues in calculus and differential equations, derivatives must be used. In general, scientists observe changing systems (dynamical systems) to determine the rate of change of a variable of interest, then incorporate this

Green’s theorem is primarily used for the integration of a line and a curved plane. The relationship between a line integral and a surface integral is demonstrated by this theorem. It is related to many theorems, including the Gauss theorem and the Stokes theorem. It is named after George Green, who published a similar finding

The process of drawing the graph (curve) of the corresponding function is known as graphing functions. Graphing basic functions such as linear, quadratic, cubic, and so on is fairly simple; however, graphing complex functions such as rational, logarithmic, and so on requires some skill and knowledge of mathematical concepts. A function graph is the collection

The process of graphing functions entails drawing the graph (curve) of the appropriate function. Graphing fundamental functions like linear, quadratic, cubic, and so on is rather simple; however, graphing complex functions like rational, logarithmic, and so on, requires some expertise and knowledge of mathematical concepts. Let’s look at how to graph functions using some examples.

Introduction Differentiation is an important concept in Mathematics that binds it with Physics. Every theorem and mathematical concept is incomplete without knowing their geometric interpretations. Thus, in this Geometric interpretations study material, we will discuss geometric interpretations of some fundamental theorems like Rolle’s Theorem and its extensions, i.e., Lagrange’s Mean Value Theorem, or simply Mean

Despite students’ best intentions to learn all of the necessary material throughout their classes, there are times when they want to know how to apply the information they’ve learned. Several mathematicians formulated the fundamental theorem of calculus, including Bhaskara, Bernoulli, Barrow, and Leibniz, although Isaac Newton’s name is most commonly linked with calculus (Gautam 130).

Introduction The fundamental theorem of Calculus is a crucial theorem in Calculus that connects antiderivatives with definite integrals. The fundamental theorem of calculus asserts that if a function f has an antiderivative F, then the definite integral of f from a to b equals F(b)-F(a). This theorem is useful for determining a function’s net change,

Exponential functions are commonly employed to model natural occurrences that rise or decrease at a pace that is proportional to the exponential function. Bacterial populations, for example, can expand at an exponential pace, as can many other types of populations. In most cases, the amount of radioactive chemicals in the environment will decline at an

Exponential smoothing is a popular family of statistical techniques and processes for discrete time series data that is used to forecast the neaIntroducti This strategy works with time series data that has seasonal components, or systematic trends were past observations were used to construct predictions.  Exponential smoothing is seen as a peer or alternative to the well-known Box jenkins ARIMA class of time series forecasting algorithms.  The methods are referred regarded as ETS models since they explicitly model Errors, Trend, and Seasonality. How does exponential smoothing operate, and what is it While the most weight is given to current observations, less weight is given to the observations immediately before them, less weight is given to the observation before that, and so on, so that weighted values follow/