Mathematical Library Methods

A user-defined method is a method defined by the user whereas library methods or built-in methods are the methods created by the developers of Java which are available in the form of packages.

(5/10) will lead to integer division as both numerator and denominator are integers. So result of (5/10) will be 0 instead of 0.5 and the entire expression will always result in 0.

ii. result = math.sqrt(b * b - 4 * a * c) / ( 2 * a );

math should be written as Math. As Java is case-sensitive so it treats math and Math differently.

Returns the absolute value of its argument. Its return type is same as the type of its arguments. For example, Math.abs(-5) will return 5.

ii. Math.sqrt()

Returns the square root of its argument as a double value. For example, Math.sqrt(25) will return 5.0.

iii. Math.cbrt()

Returns the cube root of its argument as a double value. For example, Math.cbrt(27) will return 3.0.

iv. Math.random()

Returns a positive double value, greater than or equal to 0.0 and less than 1.0.

v. Math.round()

Rounds off its argument to the nearest mathematical integer and returns its value as an int or long type. If argument is float, return type is int, if argument is double, return type is long. At mid-point, it returns the higher integer. For example, Math.round(2.5) will return 3.

vi. Math.ceil()

Returns the smallest double value that is greater than or equal to the argument and is equal to a mathematical integer. For example, Math.ceil(65.5) will return 66.0.

Math.sqrt(a + 5 * Math.pow(b, 3))

ii. The cube root of x³ + y³ + z³

Math.cbrt(x*x*x + y*y*y + z*z*z);

iii. The square root of b² + 4ac

Math.sqrt(b * b + 4 * a * c)

Math.cbrt(x * x + 5 * y * y * y)

ii. $\lvert x + y\rvert$

Math.abs(x + y)

iii. $\lvert x^3 + y^2 -2xy\rvert$

Math.abs(Math.pow(x, 3) + Math.pow(y, 2) - 2*x*y)

iv. $\frac{\pi}{6}(z^4 - 2\pi)$

Math.PI / 6*(Math.pow(z, 4) - 2*Math.PI)

v. $\sqrt[3]{z^2 - \pi}$

Math.cbrt(z*z - Math.PI)

vi. $\sqrt[4]{x^3 - y^3}$

Math.pow(x*x*x - y*y*y, 1/4)

vii. $\cfrac{amount*rate}{1 - \cfrac{1}{(1 + rate)^n}}$

(amount*rate) / (1 - (1 / Math.pow(1+rate, n)))

viii. $\frac{(-b + \sqrt{b^2 - 4ac})}{2a}$

(-b + Math.sqrt(b*b - 4*a*c)) / (2*a)

ix. $\sqrt[4]{\frac{1}{LC} - \frac{R^2}{4C^2}}$

Math.pow((1 / L*C) - ((R*R)/(4*C*C)), 1/4)

System.out.println(Math.round(14.49));

ii. Print the absolute value of -0.09

System.out.println(Math.abs(-0.09));

iii. Print the largest of -67 and -50

System.out.println(Math.max(-67, -50));

iv. Print the smallest of -56 and -57.4

System.out.println(Math.min(-56, -57.4));

v. Print a random integer between 25 and 35

int range = 35 - 25 + 1;
int num = (int)(range * Math.random() + 25);
System.out.println(num);

vi. Print 47.5 raised to the power 6.3

System.out.println(Math.pow(47.5, 6.3));

vii. Print minimum of -4, -7

System.out.println(Math.min(-4, -7));

import java.util.Scanner;

public class KboatGreatestNumber
{
    public static void main(String args[]) {
        
        Scanner in = new Scanner(System.in);
        
        System.out.print("Enter First Number: ");
        int a = in.nextInt();
        System.out.print("Enter Second Number: ");
        int b = in.nextInt();
        System.out.print("Enter Third Number: ");
        int c = in.nextInt();
        
        int g = Math.max(a, b);
        g = Math.max(g, c);
        
        System.out.println("Greatest Number = " + g);
    }
}

public class KboatNumber
{
    public static void main(String args[]) {
        int x = 81;
        int y = 3;
        
        double r1 = Math.pow(x, y);
        System.out.println("x to the power of y = " + r1);
        
        double r2 = Math.sqrt(y);
        System.out.println("Square root of y = " + r2);
    }
}

import java.util.Scanner;

public class KboatExpression
{
    public static void main(String args[]) {
        
        Scanner in = new Scanner(System.in);
        System.out.print("Enter x: ");
        int x = in.nextInt();
        System.out.print("Enter y: ");
        int y = in.nextInt();
        System.out.print("Enter z: ");
        int z = in.nextInt();
        
        double result = 1 / Math.pow(x, 2) + 1 / Math.pow(y, 3) + 1 / Math.pow(z, 4);
        
        System.out.println("Result = " + result);
    }
}

public class KboatRandom
{
    public static void main(String args[]) {
        int min = 10, max = 20;
        int range = max - min + 1;
        int num = (int)(range * Math.random() + min);
        System.out.println("Random number in the range 10 to 20: " + num);
        
        min = 25;
        max = 50;
        range = max - min + 1;
        num = (int)(range * Math.random() + min);
        System.out.println("Random number in the range 25 to 50: " + num);
    }
}

import java.util.Scanner;

public class KboatXPower
{
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        System.out.print("Enter x: ");
        int x = in.nextInt();
        System.out.print(Math.pow(x, 0) + ", ");
        System.out.print(Math.pow(x, 1) + ", ");
        System.out.print(Math.pow(x, 2) + ", ");
        System.out.print(Math.pow(x, 3) + ", ");
        System.out.print(Math.pow(x, 4) + ", ");
        System.out.print(Math.pow(x, 5));
    }
}

System.out.println(Math.abs(-999));

ii. Store the value -3375 in a variable and print its cube root.

int a = -3375;
System.out.println(Math.cbrt(a));

iii. Store the value 999.99 in a variable and convert it into its closest integer that is greater than or equal to 999.99.

double a = 999.99;
System.out.println(Math.round(a));

import java.util.Scanner;

public class KboatVelocity
{
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        System.out.print("Enter initial velocity: ");
        double u = in.nextDouble();
        System.out.print("Enter acceleration: ");
        double a = in.nextDouble();
        System.out.print("Enter distance covered: ");
        double s = in.nextDouble();
        double v = Math.sqrt(u * u + 2 * a * s);
        System.out.println("Final Velocity = " + v);
    }
}