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Discover the fascinating relationship between Chebyshev polynomials of the second kind and binomial coefficients in this exploration of series. Chebyshev Polynomials Series.
Learn what it means for a series to converge to a specific value in mathematics. Explore the concept of convergence.
Discover how to find subsets of natural numbers where the sum of reciprocals of their squares is equal exploring both finite and infinite cases.
Learn about arithmetic geometric and harmonic series with 5 examples each. Discover the formulas and how to solve problems.
Discover the fascinating exponential limit of x^x as x approaches 0+. Learn the solution using logarithms and L'Hôpital's rule.
Learn how to calculate distance in 3D using triangular relationships and trigonometric ratios.
Discover Sophie Germain primes special prime numbers with unique properties. Learn about their relation to safe primes applications in cryptography and how to identify them using Python.
Prove the equality of cosine series in generalized functions. Learn how to manipulate trigonometric series for advanced applications.
Calculate the limit of cos(√x) raised to the power of 1/x as x approaches 0 from the right. Learn the Taylor expansion method for solving this type of limit problem.
Find the limit of a trigonometric expression as x approaches 0. Learn how to use trigonometric identities to solve this problem.
Learn about vectors in mathematics their properties and how they’re used in physics computer graphics and machine learning.
Learn various methods for proving mathematical statements including direct proof indirect proof (contradiction and contrapositive) proof by cases and mathematical induction. Explore examples and applications.
Conquer the CBSE Board Exams 2025 with our guide! Learn effective study strategies, time management tips, and overcome exam anxiety for success.
The six trigonometric functions are defined below. Refer to the above diagram to get the relational picture. sinθ = \( \dfrac {\mathrm{perpendicular}} {\mathrm{hypotenuse}} = \dfrac {p}{h} \) cosθ = \( \dfrac {\mathrm{base}} {\mathrm{hypotenuse}} = \dfrac {b}{h}...
Pythagoras’ theorem is stated as : The sum of the areas of the two squares on the perpendicular(p) and base(b) of a right-angle triangle is equal to the area of the square on the hypotenuse(h). i.e. p2 + b2 = h2
A right-angle triangle is a triangle in which one of the angles measures 90°. Right-angled triangles have wide applications in mathematics and physics and as such, it became convenient to have specific names for their sides so that the problem statement in mathematics...
The trigonometric functions can be described on an x-y coordinate plane (Euclidean plane) using a circle of radius 1 unit and cutting a sector that subtends an angle θ at the centre. Refer to the diagram below for details.