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The asinh() function is a function of standard C++ library. The asinh(value) is an inverse hyperbolic sine that returns the value of sinh(x) where x is in radian.The function −asinh() ;Parameter to the function, inverse hyperbolic angle in radian . It can be negative, positive or zero. The parameter value can be double, float or long double.Return value − It returns the inverse hyperbolic sine value of the input value. The returned value is in radians.Lets see an example that shows the working of the function −Example#include using namespace std; int main() { double insinh = 75.0; double ... Read More
Symmetric Matrix − A matrix whose transpose is equal to the matrix itself. Then it is called a symmetric matrix.Skew-symmetric matrix − A matrix whose transpose is equal to the negative of the matrix, then it is called a skew-symmetric matrix.The sum of symmetric and skew-symmetric matrix is a square matrix. To find these matrices as the sum we have this formula.Let A be a square matrix. then, A = (½)*(A + A`)+ (½ )*(A - A`), A` is the transpose of the matrix.(½ )(A+ A`) is symmetric matrix.(½ )(A - A`) is a skew-symmetric matrix.Example#include using namespace std; ... Read More
The sum of square-sums of the first n natural numbers is finding the sum of sum of squares upto n terms. This series finds the sum of each number upto n, and adds this sums to a sum variable.The sum of square-sum of first 4 natural numbers is −sum = (12) + (12 + 22 ) + (12 + 22 + 32) + (12 + 22 + 32 + 42 ) = 1 + 5 + 14 + 30 = 50There are two methods to find the sum of square-sum of first n natural numbers.1) Using the for loop.In this ... Read More
The series of squares of first n odd numbers takes squares of of first n odd numbers in series.The series is: 1,9,25,49,81,121…The series can also be written as − 12, 32, 52, 72, 92, 112….The sum of this series has a mathematical formula −n(2n+1)(2n-1)/ 3= n(4n2 - 1)/3Lets take an example,Input: N = 4 Output: sum =Explanation12 + 32 + 52 + 72 = 1 +9+ 25 + 49 = 84Using formula, sum = 4(4(4)2- 1)/3 = 4(64-1)/3 = 4(63)/3 = 4*21 = 84 both these methods are good but the one using mathematical formula is better because it does not use looks which reduces its time complexity.Example#include int main() { int n = 8; int sum = 0; for (int i = 1; i
The HTML DOM Input Reset type property is associated with the input element having its type=”reset”. It will always return reset for the input reset element.SyntaxFollowing is the syntax for reset type property −resetObject.typeExampleLet us look at an example for the reset type property − Input reset type Property UserName: Location: Get the above input element type by clicking the below button GET Type function resetType() { var P=document.getElementById("RESET1").type; document.getElementById("Sample").innerHTML = "The type for the input field is: "+P ; } ... Read More
A Set is a collection of data elements. Subset of a set is a set formed by only the elements after parent set. for example, B is A subset of a if all elements of B exist in A.Here we need to find the sum of all subsets of a set found by first n natural numbers. this means I need to find all subsets that can be formed and then adding them. Let's take an example, N = 3Set = {1, 2, 3}subsets formed = { {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3, } ... Read More
An arithmetic progression (AP) is a series of numbers in which the difference between two consecutive terms in the same. The difference is calculated by subtracting the second term from the first.Let's take a sample sequence to know about AP, 5, 7, 9, 11, 13, 15, . . . The common difference(d) of this arithmetic progression is 2. This means every succeeding element differs the former one by 2. The first term (a) of this series is 5.The general formula for finding the nth term is a{n} = a + (n-1)(d)In this problem, we are given an AP and we ... Read More
A series is a sequence of numbers that have some common traits that each number follows. There are various series defined in mathematics with sum mathematical logic or mathematical formula. In this problem we are given a series of numbers 2/3 , -4/5 , 6/7 , -8/9 , …..The general term of the series can be defined as (-1)n *(2*n)/ ((2*n)+1)To find the sum of series, we need to add each element of the given series as, 2/3 - 4/5 + 6/7 - 8/9 + ……Let's take an example, Input: 10 Output: -0.191921Explanation(2 / 3) - (4 / 5) + ... Read More
A series is a sequence of numbers that have some common traits that each number follows. These mathematical series are defined based on some mathematical logic like every number increases by the same interval( arithmetic progression), every number is increased by the same multiple( geometric progression), and many other patterns.To find the sum of a series we need to evaluate the series and make a general formula for it. But in the series that is no common declaration that takes place so we have to go through the classical approach by adding each number of the series to a sum ... Read More
The HTML DOM Input Reset object is associated with the element with type “reset”. We can create and access an input element with type reset by using the createElement() and getElementById() method respectively.PropertiesFollowing are the properties for the Input reset object −PropertyDescriptionautofocusTo set or return if the reset button should get focus automatically when the page loads or not.defaultValueTo set or return the reset button default value.disabledTo set or return if the reset button has been disabled, or not.formTo return the reference of the form containing the reset button.nameTo set or return the name attribute value of the reset ... Read More