Class 12

Mathematical calculus relies heavily on Lagrange’s mean value theorem. Parmeshwara, an Indian mathematician from Kerala, initially proposed the mean value theorem in its original form in the 14th century. Rolle’s Theorem, a simpler version of this, was proposed by Rolle’s in the 17th century and proved solely for polynomials. Also, in the year 1823, Augustin […]

It is known as Bernoulli’s rule, and it is a mathematical theorem that is used to evaluate the limits of indeterminate forms. In honor of the French philosopher L’Hôpital, who presented the rule for the first time in the 18th century, it was given this name. Using the rule (or using it again and again)

Determining the type of operator used to connect two functions is an important part of the differentiation process. For example, if a +ve sign is used to indicate a difference between two functions, then those two functions can be distinguished from one another. In contrast, multiplication and division are not able to be done this

Differentiation is much needed to find the rate of change. It all starts with the differentiation of a single variable into a higher order of variables. The slope of a tangent line indicates a graph of the function at any point. Differentiation applies to several different variables. Differentiation can be done for implicit functions by

To find the derivative or differentiation of a function given as a ratio or division of two differentiable functions, one can use the calculus quotient rule. Because both f(x) and g(x) are differentiable, we can use the formula f(x) g(x) for the derivative of a function of the form f(x)/x, where g(x) > 0. After

Introduction Compared to a straight line, the slope of a curve changes as you walk along with the graph. Calculus teaches students that each point on this graph can be defined by a slope, often known as an “instantaneous rate of change.” The tangent line is a straight line with that slope passing through that

One of the most prominent applications of differentiation is the “tangent line.” Tangent is derived from the Latin word “tangere,” which means “to touch.” At one point on the curve, the tangent line hits it. To calculate the tangent line equation, we must first determine the curve’s equation (which is given by a function) and

A curve’s asymptote is the point at which the curve converges. In other words, the curve and its asymptote approach each other infinitely but never meet. Asymptotes are useful for charting rational equations and are used in big O notation. They are also easy approximations to complex equations. Understanding the meanings of vertical, horizontal, and

Archimedes expected modern calculus and evaluation by way of applying the concept of the infinitely small and the approach of exhaustion to derive and show a number of geometrical theorems, consisting of the Area of a circle; the surface area and volume of a sphere; parabola of an area of an ellipse;  the area beneath

Introduction Derivatives is the most important topic of mathematics. It is often involved in numerous types of calculations. It helps determine the rate of change of function with respect to a variable. The application of derivatives is helpful to determine the rate of change of a quantity, calculate the approximate value, find the equation of