Applications of Derivatives

Number System Conversion

As we all know, the number system is a way of expressing numbers in a structured manner. In number system conversion, we will look at how to convert a number from one base to another base using a different base system. There are many different number systems that can be used, including binary numbers, decimal […]

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Applications of Derivatives, Class 12, IIT JEE, Increasing and decreasing functions, Maths

Newton-Leibniz Formula

Differentiation and integration play a very important part in the mathematical studies of higher-order. And, in their very concept, they cover a very large basis for their varied applicability.  The method of Newton-Leibnitz is used to solve the definite integrals, but of higher difficulties, the ones in which the limit for the integral in itself

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Applications of Derivatives, Class 12, IIT JEE, Increasing and decreasing functions, Maths

Multiplication Tricks

Introduction: Long and difficult multiplication problems necessitate the use of multiplication tricks. Multiplication is simple for single-digit, two-digit, and even three-digit integers. It takes a long time to solve higher numbers with more digits, such as 4, 5, 6, 7, and so on. As a result, we’ll learn some magic maths tactics for quick calculations

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Applications of Derivatives, Class 12, IIT JEE, Increasing and decreasing functions, Maths

Logarithmic Functions

Introduction Many mathematicians have utilised logarithms to convert multiplication and division problems into addition and subtraction problems before the discovery of calculus. The power of some numbers (typically, the base numbers) is raised to obtain another number in logarithms. It is the reciprocal of the exponential function. The inverses of exponential functions are logarithmic functions,

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Applications of Derivatives, Class 12, IIT JEE, Increasing and decreasing functions, Maths

Logarithmic Function

In mathematics, prior to the development of calculus, many mathematicians relied on logarithms to convert multiplication and division problems into addition and subtraction problems. This was done before calculus was discovered. To arrive at a different number using logarithms, the power is multiplied by some numbers (often, the base number). It is the complement of

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Applications of Derivatives, Class 12, IIT JEE, Increasing and decreasing functions, Maths

Logarithmic and Exponential Functions

Logarithmic and exponential functions are quite significant aspects of mathematics. This stands true both in mathematical theory and practice. It is possible to express any exponential function in the logarithmic form. Similarly, you can write down all logarithmic functions in the exponential form. An exponential equation is one in which the appearance of the variable

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Applications of Derivatives, Class 12, IIT JEE, Increasing and decreasing functions, Maths

Log base 2

Many mathematicians used logarithms to transform multiplication and division problems into addition and subtraction problems prior to the calculus era. The power is raised to some numbers in logarithms, which is usually the base number. Then it can return a different number. It is the exponential function’s inverse function. The log Base 2 Binary base

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Applications of Derivatives, Class 12, IIT JEE, Increasing and decreasing functions, Maths

Limits of Polynomial and Branch Functions

A polynomial function contains only positive integer exponents like the quadratic equation or the cubic equation. For instance, 2x+5 is a polynomial with an exponent of 1. In general, a polynomial function is sometimes referred to as a polynomial or polynomial expression, depending on its degree. Any polynomial’s degree is the highest power it contains.

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Applications of Derivatives, Class 12, IIT JEE, Increasing and decreasing functions, Maths

Limits at infinity and infinite limits

What is the limit? The limit of a function f(x) can be defined as the value; the function f(x) approaches as the value of x approaches a certain x = k value. We represent the limit of the function f(x) as the value of x tends to k as, xkf(x)= C Here, the value of

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Applications of Derivatives, Class 12, IIT JEE, Increasing and decreasing functions, Maths

Limitations of Squeeze Theorem

We may have encountered various theorems in Calculus, particularly when determining the difficult limits and derivatives of functions. We use a variety of theorems and formulas to discover the limits of different types of functions, but we always strive to find the simplest way to solve them so that we can reach the answer quickly.

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Applications of Derivatives, Class 12, IIT JEE, Increasing and decreasing functions, Maths