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Mathematical Problems Articles
Found 12 articles
How to ace math exams simple tips and tricks
In this article, you will learn simple tips and tricks to ace math exams on the fly. Although there are no shortcuts to success, focused study, regular practice of solving examples and worksheets, mastering the concepts are some of the best practices."If I were again beginning my studies, I would follow the advice of Plato and start with mathematics." Galileo GalileiStay Focused and Never Give-upWhen you study math, find a quiet place, get rid of the distractions, and focus on your work. You can easily make a mistake or miss a number otherwise.Understand and Master the ConceptsWhichever topic you are ...
Read MoreSecant method to solve non-linear equation\\n
Secant method is also used to solve non-linear equations. This method is similar to the Newton-Raphson method, but here we do not need to find the differentiation of the function f(x). Only using f(x), we can find f’(x) numerically by using Newton’s Divide difference formula. From the Newton-Raphson formula, we know that, Now, using divide difference formula, we get, By replacing the f’(x) of Newton-Raphson formula by the new f’(x), we can find the secant formula to solve non-linear equations.Note: For this method, we need any two initial guess to start finding the root of non-linear equations.Input and OutputInput: The ...
Read MoreTrapezoidal Rule for definite integral
Definite integrals can be solved using this trapezoidal rule. To integrate a function f(x) between the range a to b is basically finding the area below the curve from point x = a to x = b. To find that area, we can divide the area into n trapezoids, and the width of each trapezoid is h, so we can say that (b - a) = nh. When the number of trapezoids increases, the result of area calculation will be more accurate. To solve integrals, we will follow this formula.Here h is the width of the interval, and n is the ...
Read MoreLinear Regression
From a given set of data points, the linear regression finds an equation of straight line. The given points will follow the straight line. Using this formula, we can predict what will be the value for some other specific point, which is not present in the set currently.For solving linear regression problems using some data points, we have to follow these formulae:Here the m and c are the slope and the y-intercept respectively. Using these expressions, we can get the equation of straight line in this form: 𝑦 = 𝑚𝑥 + 𝑐.Input and OutputInput: The (x, y) coordinates of some ...
Read MoreSimpson's 1/3 Rule for definite integral
Like the Trapezoidal Rule, Simpson’s 1/3rd rule is also used to find the integral value from the range a to b. The main difference between trapezoidal and the Simpson’s 1/3rd rule is, in the trapezoidal rule, the whole sections are divided into some trapezoids, but in this case, each trapezoid are also divided into two parts.For this rule, we will follow this formula:Here h is the width of the interval, and n is the number of intervals. We can find the h by using Input and OutputInput: The function f(x): (x+(1/x). The lower and upper limit: 1, 2. The number of ...
Read MoreRunge-Kutta 4th order rule for differential equation
Runge Kutta method is used for solving ordinary differential equations (ODE). It uses dy/dx function for x and y, and also need the initial value of y, i.e. y(0). It finds the approximate value of y for given x. For solving ODE, we have to follow these formulas:Here h is the height of the interval.Note: From these formulas, we can use first two k1 and k2 find the Runge-Kutta 2nd Order solution for ODE.Input and OutputInput: The x0 and f(x0): 0 and 0 the value of x = 0.4 the value of h = 0.1 Output: Answer of differential equation: ...
Read MoreLagrange Interpolation
For constructing new data points within a range of a discrete set of given data point, the interpolation technique is used. Lagrange interpolation technique is one of them. When the given data points are not evenly distributed, we can use this interpolation method to find the solution. For the Lagrange interpolation, we have to follow this equation.Input and OutputInput: List of x and f(x) values. find f(3.25) x: {0, 1, 2, 3, 4, 5, 6} f(x): {0, 1, 8, 27, 64, 125, 216} Output: Result after Lagrange interpolation f(3.25) = 34.3281AlgorithmlargrangeInterpolation(x: array, fx: array, x1)Input − x array and fx ...
Read MoreDecimal to Binary conversion\\n
A decimal number can also be converted into its binary form. To convert a decimal number to binary number, we need to divide the number by 2 until it reaches 0 or 1. And in each step, the remainder are stored separately to form the binary equivalent number in reverse order.In this algorithm, we will follow the recursive approach. It will help us to solve the problem without using stack data structure. In the implementation, we know that recursion of a function will follow the internal stack. We will serve our job by using that stack.Input and OutputInput: Decimal number ...
Read MoreLucky Numbers
Lucky numbers are some special integer numbers. From basic numbers, some special numbers are eliminated by their position. Instead of their value, for their position, the numbers are eliminated. The numbers which are not deleted, they are the lucky numbers.The number deletion follows some rule. At first, every second number are deleted, after that, all 3rd numbers are deleted and so on.Here is some example −1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 (1 – 25 all) 1 3 5 7 9 11 ...
Read MoreFind GCD of two numbers
In mathematics, Greatest Common Divisor (GCD) is the largest possible integer, that divides both of the integers. The condition is that the numbers must be non-zero.We will follow the Euclidean Algorithm to find the GCD of two numbers.Input and OutputInput: Two numbers 51 and 34 Output: The GCD is: 17AlgorithmfindGCD(a, b)Input: Two numbers a and b.Output: GCD of a and b.Begin if a = 0 OR b = 0, then return 0 if a = b, then return b if a > b, then return findGCD(a-b, b) ...
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