Welcome to the advanced math problems tutorial section! Here, you will find a variety of challenging problems to enhance your mathematical skills. Whether you are a student, teacher, or simply a math enthusiast, these problems are designed to stretch your mind and push the boundaries of your knowledge.
Problem Set 1: Calculus
Problem 1.1
Evaluate the integral: $$\int_{0}^{\pi} \sin^2(x) , dx$$
Problem 1.2
Find the derivative of the function: $$f(x) = e^{x^2} \sin(x)$$
Problem Set 2: Algebra
Problem 2.1
Solve the equation: $$x^3 - 6x^2 + 11x - 6 = 0$$
Problem 2.2
Prove the identity: $$\frac{1}{a^2 + b^2} + \frac{1}{b^2 + c^2} + \frac{1}{c^2 + a^2} = 1$$
Problem Set 3: Geometry
Problem 3.1
Calculate the area of a regular hexagon with a side length of 10 units.
Problem 3.2
Find the volume of a sphere with a radius of 5 units.
Resources
For more advanced math problems and tutorials, check out our Advanced Math Resources page.
Here's a visual representation of a complex number, which is often used in advanced math problems: