1. What is the name of the mathematical concept that describes the smoothness of a function?

The name of the mathematical concept that describes the smoothness of a function is differentiability.

2. What is the limit of (sin x)/x as x approaches 0?

The limit of (sin x)/x as x approaches 0 is 1.

3. What is the formula for calculating the surface area of a sphere?

The formula for calculating the surface area of a sphere is 4πr^2, where r is the radius of the sphere.

4. What is the mathematical constant e equal to?

The mathematical constant e is equal to approximately 2.71828.

5. What is the Pythagorean Theorem and how is it used?

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It is used to find the length of one side of a right triangle if the lengths of the other two sides are known.

6. What is the difference between a rational and an irrational number?

A rational number is a number that can be expressed as a ratio of two integers, while an irrational number is a number that cannot be expressed as a ratio of two integers. Irrational numbers are non-repeating and non-terminating decimals.

7. What is the formula for finding the derivative of a function?

The formula for finding the derivative of a function is f'(x) = lim(h→0) [f(x+h) - f(x)]/h.

8. What is the sum of the angles in a triangle?

The sum of the angles in a triangle is 180 degrees.

9. What is the area of a circle with a radius of 5 inches?

The area of a circle with a radius of 5 inches is 78.5 square inches (rounded to one decimal place).

10. What is the formula for calculating the volume of a cone? Give a detailed answer, with examples and references if possible.

The formula for calculating the volume of a cone is (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone. For example, if a cone has a radius of 4 inches and a height of 6 inches, its volume would be (1/3)π(4^2)(6) = 32π cubic inches.