Exponential functions can be differentiated using the chain rule. One of the most intriguing and functional characteristics of the natural exponential function is that it is its own derivative. In other words, it has solution to the differential equation being the same such that,y’ = y.The exponential function which has the property that the slope … Read more

The function defined by f(x) = bx; (b>0), b≠1) is called an exponential function with base b and exponent x.Here, the domain of f can be explained as a set of all real numbers. Let m and n be positive numbers and let a and b be real numbers. Then, The exponential function y = bx (b> … Read more

Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions and differentiability The derivative does not exist (the function is not differentiable) at any point where the function is not continuous. Therefore, if the function is not continuous it’s also not differentiable. But even if the function … Read more

Consistency, inconsistency and number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables using the inverse of a matrix A linear equation multiple variables: x, y, z etc. is an equation of the form: ax + by + cz = p, where a, b, … Read more

Arithmetic Mean The A.M or the Arithmetic Mean is referred to as the average of 2 given numbers. And if one A.M “A” is included between the two numbers which are “a” & “b”, then A is called the arithmetic mean present in between the numbers, a & b. A.M. = A = $\frac{a+b}{2}$ Here, … Read more

Arithmetic and Geometric series infinite G.P. and its sum If there’s a sequence 10, 20, 30, 40, then each term is 10 more than the earlier term. This is the example of the (AP) Arithmetic Progression & a constant value which clearly describes the difference in between any 2 consecutive terms which is known as … Read more

Calculating averages for various series had been a part of most of the mathematics practices well, like the arithmetic mean, the geometric mean of series and sequences could be worthwhile calculations. Geometric Mean As the name suggests, the geometric mean formula is useful for calculating the geometric mean of a considerable set of numbers. Recall … Read more

There is absolutely much to know about series and sequences that may be effective for dealing with various events taking place in regular lives and other areas of professional working. Geometric Progression In a sequence of terms, if each term is observed to be a constant multiple of the preceding term, the sequence is then … Read more

If the sequence is geometric, then without really adding all the actual terms, there are methods for finding the sum of 1st n terms, which are denoted by Sₙ. With the use of the formula, you can find the sum of the first Sₙ terms of the geometric sequence Sn = a₁(1−rⁿ) / 1−r, r≠1 … Read more

You may have already been introduced to finding averages. Well, arithmetic mean is just that. Understanding Arithmetic Mean In general language, average data and arithmetic mean are synonymous. It could also be referred to as the representative value for a group of data. Suppose that you have been given n number of elements and required … Read more