Search This Blog

Friday, April 9, 2021

When Your Math Professor is a Conspiracy Theorist

Prove that the Probability of the Impossible Event is Zero

Probability Proof using the Probability Axioms

Prove that the Probability of Any Event is Between 0 and 1

How to Solve the Bernoulli Differential Equation y' + xy = xy^2

Prove that Probability of the Complement of A is One Minus the Probabili...

Find a Formula for the Geometric Mean G and log(G) given Data and Their ...

Prove that if z_i = x_i + y_i then the Arithmetic Mean of Z is the Sum o...

Prove the Identity for the Finite Sums SUM((x + a)(y + b))

How to Prove an Identity Involving Finite Sums

Learn How to Prove an Identity with Finite Sums and Variables

Inverse Laplace Transform of s/((s - 2)^2 + 9)

Inverse Laplace Transform of (s + 1)/(s^2 - 9)

Inverse Laplace Transform of 5s/(s^2 + 1)^2

How to Find the Derivative of y = e^(tant) using the Chain Rule

Learn How to Use the Chain Rule Example with y = (3x^2 + 7x)^10

Inverse Laplace Transform of 1/sqrt(s)

Prove that the Root Mean Square is Greater Than the Geometric Mean for T...

Inverse Laplace Transform of 1/(s - 8)

Inverse Laplace Transform of 1/(s^2 - 2s + 9)

How to Solve the Linear Third Order Differential Equation y''' - 6y'' + ...

How to Find the Laplace Transform of t*e^(4t)

Inverse Laplace Transform of s/(s^2 + 6)

How to Find the Inverse Laplace Transform of (s + 4)/(s^2 + 4s + 8)

Prove that the Sum of the Deviations of a Data Set from Their Mean is Zero

How to Solve the Linear Differential Equation y' - 5y = 0

Learn How to Find the Harmonic Mean of Numbers

How to Find the Quadratic Mean (R.M.S.) of a Set of Numbers

Learn How to Find the Geometric Mean of a List of Numbers

Find the Root Mean Square (Quadratic Mean) of the Numbers

How to Find the Harmonic Mean of a List of Numbers

How to Find the Geometric Mean of a List of Numbers

How to Find the Mean, Median, and Mode of a Set of Data

How to Find the Median of a Set of Grades by Hand Without a Calculator

Find the Harmonic Mean of the Numbers

Learn How to Express Sums in Summation Notation

Learn How to Find the Weighted Mean of Grades

Learn How to Write Out the Terms of a Finite Sum

How to Find the Arithmetic Mean of The Grades on an Exam

Learn How to Find the Root Mean Square of Numbers (Quadratic Mean)

Learn How to Find the Harmonic Mean of a Data Set

How to Find the Geometric Mean of a Data Set

Axioms of Probability

How to Simplify the Square Root of 36: sqrt(36)

How to Simplify the Square Root of 8: sqrt(8)

How to Simplify the Square Root of 80: sqrt(80)

How to Simplify the Square Root of 27: sqrt(27)

How to Simplify the Square Root of 25: sqrt(25)

How to Simplify the Square Root of 16: sqrt(16)

How to Simplify the Square Root of 9: sqrt(9)

How to Simplify the Square Root of 4: sqrt(4)

How to Simplify the Square Root of 84: sqrt(84)

How to Compute the Square Root of 64: Sqrt(64)

How to Compute the Square Root of 49: Sqrt(49)

How to Simplify the Square Root of 98: sqrt(98)

How to Simplify the Square Root of 96: sqrt(96)

How to Simplify the Square Root of 92: sqrt(92)

How to Simplify the Square Root of 88: sqrt(88)

How to Compute the Square Root of 104: Sqrt(104)

How to Simplify the Square Root of 100: sqrt(100)

How to Simplify the Square Root of 99: sqrt(99)

How to Find the Arithmetic Mean given Data and Their Frequencies

Find the Arithmetic Mean of a Student's Grades

Find the Weighted Mean

Find the Geometric Mean (Several Examples)

How to Find the Derivative of y = csc(e^x) using the Chain Rule

How to Simplify the Square Root of 81: sqrt(81)

How to Simplify the Square Root of 76: sqrt(76)

How to Compute the Square Root of 75: Sqrt(75)

How to Compute the Square Root of 72: Sqrt(72)

How to Compute the Square Root of 68: Sqrt(68)

How to Simplify the Square Root of 45: sqrt(45)

Find the Quadratic Mean (Root Mean Square) of a List of Numbers

How to Simplify the Square Root of 90: sqrt(90)

Saturday, April 3, 2021

This Easy Trick Will Make You Better at Math - And You Might Not be Doin...

Prove that 1/2 + 1/4 + 1/8 + ... + 1/2^(n - 1) is less than 1

How to Multiply Matrices: Three Examples with Row and Column Matrices

How to Prove a Number is an Algebraic Number, Example with cuberoot(3)/2

Prove that the there is No Rational Number Whose Square is 2

Prove that sqrt(2) + sqrt(3) Cannot be a Rational Number

Prove that the Product of Invertible Matrices is Invertible and (AB)^(-1...

Prove that the Square of any Odd Integer is Odd

Prove that Every Rational Number is Algebraic

Induction Proof: x^n - y^n has x - y as a factor for all positive intege...

Friday, April 2, 2021

How to Write a Complex Number in Polar Form, Example with 3 + 3i

Prove that if A is an Invertible Matrix then AB = AC Implies B = C

How to Understand the Definition of Matrix Multiplication(Useful for Wri...

Prove that Matrix Multiplication Distributes Over Addition: A(B + C) = A...

Prove the Infinite Geometric Series Formula: Sum(ar^n) = a/(1 - r)

Prove that the Set of All Rational Numbers Between 0 and 1 Inclusive is ...

Explain Why 1/0 is Not Considered a Number

Simplify the Complex Number (i + i^2 + i^3 i^4 + i^5)/(1 + i)

Simplify the Difference in the Modulos |1/(1+3i) - 1/(1 - 3i)|

How to Solve the Cubic Equation x^3 - 2x - 4 = 0

Simplify the Product of the Moduli |3 - 4i|*|4 + 3i|

Use the Definition of Convergence to Prove that the Sequence {c/n^p} Con...

How to Multiple Matrices, Example with a 2 x 3 Times a 3 x 4

How to Add and Substract Matrices, Two Examples

Simplify the Rational Expression (x^2 - 5x + 6)/(x^2 - 2x - 3)

How to Prove a Number is an Algebraic Integer, Example with 5 + 13sqrt(2)

Prove that the Functions sin(x), cos(x), and x are Linearly Independent ...

Write cos(theta) in terms of sin(theta) if theta is acute

How to Evaluate Functions

Prove the Inequality of Arithmetic and Geometric Means (AM-GM inequality)

How to Determine if a Matrix is Symmetric or Skew-Symmetric

Find x and B if B is a Symmetric Matrix

Prove that Scalar Multiplication Distributes over Matrix Addition

How to Find the Transpose of a Matrix, 4 Examples

How to Determine if Two Vectors are Linearly Dependent

Write sin(theta) in terms of cot(theta) if theta is in quadrant 3

Why is 0/0 Not a Number?

Write the First Five Terms of the Sequence {(-1)^(n -1)/(2 * 4 * 6 *...*...

Proof That Matrix Addition is Associative

People Who Do Well in Math Do This

How to Prove a Number is an Algebraic Number: Example with cuberoot(2) +...

Wednesday, March 31, 2021

Induction Inequality Proof: 2^n greater than n^3

How to Find the Simple Interest and the Future Value of the Account

Verify the Trigonometric Identity (cos^2(x) - tan^2(x))/sin^2(x) = cot^2...

Find the y-coordinate of the Point on the Unit Circle

Give an Example of Two Discontinuous Functions Whose Sum is Continuous

Sum of the Infinite Series 1/p - 1/p^2 + 1/p^3 - 1/p^4 + ...

How to Find the Derivative of 1/sqrt(x) using the Definition of the Deri...

How to Find the Future Value of an Annuity, The Personal Contribution, a...

Solve the Equation for r in the Infinite Geometric Series

Find the Sum of the Series SUM((2^n + 1)/3^n)

Determine if the Piecewise Function is Continuous by using the Definitio...

How to Find and Simplify the Difference Quotient for the Cubic Function ...

Learn How to Find the Limit of a Piecewise Function

Find the Value of b so that the Limit of the Piecewise Function Exists

How to Find the Simple Interest and the Future Value of the Account

Find the Sum of the Infinite Geometric Series 1/p + 1/p^2 + 1/p^3 + ...

How to use Implicit Differentiation to find dp/dx for p^2 + p + 2x = 40

Is the Function G(x) = 1/x Continuous at x = 0? Why or Why Not?

How to Find and Simplify the Difference Quotient for the Quadratic Funct...

Determine if the Function g(x) = x^2 - 3x is Continuous at x = 4 and Exp...

Find the Average Rate of Change of h(x) = 1/x from x_1 = 4 to x_2 = 8

Find the One Sided Limits and the Regular Limit Given the Piecewise Func...

Improper Integral of 3*e^(-3x) from 0 to Infinity

Learn How to Find the Derivative of an Exponential Function with Base 20

How to Find a Limit by using the Definition of the Derivative

Prove that Every Group Homorphism Maps the Identity Element to the Ident...

How to Find the Derivative of y = e^x * x^e using the Product Rule from ...

Find the Interval and Radius of Convergence of the Power Series (Geometr...

Graph the Hyperbola x^2 - y^2 = 1 and Find the Domain and Range

Find the Derivative of y = ln(7x), Example using the Product Rule for Logs

Find the Derivative of y = 2^(3 + sin(x)), Example with a Base 2 Exponen...