surya_latex

Below are ten mathematical formulas explained:

• This is the Pythagorean theorem, where a and b are the lengths of the two shorter sides of a right triangle, and c is the length of the hypotenuse.

• This is the derivative of the exponential function e^x with respect to x. It equals the exponential function itself.

• This represents the definite integral of a function f(x) from a to b. It calculates the area under the curve of f(x) between a and b.

• This is the formula for the sum of the first n positive integers. It's also known as the arithmetic series formula.

• This is the binomial coefficient formula, which calculates the number of ways to choose k items from a set of n items without regard to the order.

• This is the derivative of the sine function with respect to x, which equals the cosine function.

• This is Euler's formula, which relates the exponential function with trigonometric functions. i is the imaginary unit.

• This notation represents the limit of a function f(x) as x approaches a which equals L.

• This is the power rule for differentiation, which gives the derivative of x^n with respect to x.

• This is the power rule for integration, which gives the antiderivative of x^n with respect to x.