Enjoy learning mathematics

Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.

-Archimedes-

Solved Exercises

Solved Exercises

Mathematics problems with solutions

Proof Without Words

Mathematics facts that you did not see in school
Visual mathematics

Books

A collection of books that can make you fall in love with mathematics

The Beauty of Mathematics : It Can Never Lie to You

Mathematics is the queen of the sciences.

Carl Friedrich Gauss

To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.

Leonhard Euler

There is geometry in the humming of the strings, there is music in the spacing of the spheres.

Pythagoras

Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.

Nikola Tesla

Solved Problems

Choose a problem to access the corresponding solution.

Find the volume of the square pyramid as a function of \(a\) and \(H\) by slicing method.

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Prove that \[\lim_{x \rightarrow 0}\frac{\sin x}{x}=1\]

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Prove that

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Calculate the half derivative of \(x\)

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Prove Wallis Product Using Integration

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Calculate the radius R

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Calculate the volume of Torus using cylindrical shells

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Find the derivative of exponential \(x\) from first principles

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Calculate the sum of areas of the three squares

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Find the equation of the curve formed by a cable suspended between two points at the same height

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Solve the equation for real values of \(x\)

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Solve the equation for \(x\epsilon\mathbb{R}\)

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Determine the angle \(x\)

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Calculate the following limit

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Calculate the following limit

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Calculate the integral

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Challenging problem

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Speechless proof

Explanation

Prove that

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Prove that \(e\) is an irrational number

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Find the derivative of \(y\) with respect to \(x\)

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Find the limit of width and height ratio

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How Tall Is The Table ?

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Why 0.9999999...=1

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Solve the equation for \(x \in \mathbb{R}\)

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Is the walk possible?

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Calculate the following

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Is \(\pi\) an irrational number ?

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How far apart are the poles ?

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Solve for \(x \in \mathbb{R}\)

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What values of \(x\) satisfy this inequality

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Prove that the function \(f(x)=\frac{x^{3}+2 x^{2}+3 x+4}{x} \) has a curvilinear asymptote \(y=x^{2}+2 x+3\)

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Why does the number \(98\) disappear when writing the decimal expansion of \(\frac{1}{9801}\) ?

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Only one in 1000 can solve this math problem

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Error to avoid that leads to:

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What's the problem ?

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Explain your answer without using calculator

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Determine the square's side \(x\)

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Find out what is a discriminant of a quadratic equation.

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Calculate the rectangle's area

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Infinitely nested radicals

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Determine the square's side \(x\)

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Wonderful math fact: 12542 x 11 = 137962

Explanation

Find the volume of the interior of the kiln

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Calculate the sum

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What is the new distance between the two circles ?

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Calculate the area of the Squid Game diagram blue part

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Calculate the limit

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Find the infinite sum

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Calculate the integral

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Prove that

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Can we set up this tent ?

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Find the value of \(h\)

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Find the length of the black segment

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Prove that pi is less than 22/7

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Find the value of \(x\)

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Amazing !

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Prove that

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What is the weight of all animals ?

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Determine the length \(x\) of the blue segment

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How many triangles does the figure contain ?

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If we draw an infinite number of circles packed in a square using the method shown below, will the sum of circles areas approach the square's area?

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What is the value of the following infinite product?

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Which object weighs the same as the four squares?

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What is \((-1)^{\pi}\) equal to?

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Can you solve it?

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Can you solve it?

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Great Math Problem

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Calculate the integral \(\int_{0}^{1}(-1)^{x} d x\)

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Find the general term of the sequence

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Find the radius of the blue circles

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Determine the area of the green square

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Find the area of the square

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Calculate the integral

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Calculate the integral

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Calculate

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What is the radius of the smallest circle ?

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Find the Cartesian equation of the surface

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Calculate the integral

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Calculate the limit

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Can you solve this ?

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Solve the quintic equation for real \(x\)

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How many students study no language ?

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Probability of seeing a car in 10 minutes

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What is the number of where the car stands ?

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What is the value of \(x\) ?

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Prove that

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Is it possible to solve for \(x\) so that \(ln(x)\), \(ln(2x)\), and \(ln(3x)\) form a right triangle?

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How many times will circle A revolve around itself in total ?

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Find the distance \(BC\)

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Solve for a^6, a : positive number

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Solve the quadratic equation by Completing the Square

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Prove that

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The area of a circle by slicing

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Determine the length and width of the rectangular region of the house

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a+b=20, find the maximum value of a²b

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Why 1+2+3+4+... is not equal to -1/12

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Elon Musk's interview question

Solution

Proof of Thales' Theorem

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How to check if two line segments intersect?

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What is the minimum number of operations required to reach 100?

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Fundamental Theorem of Calculus

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"100 doors" problem

Solution

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