Mathematics - Eat it up!

15 Points Per Correct Answer - No time limit  

1. The famous Pythagorean Theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse, is actually a special case of what theorem/law? Sine Law Cosine Law Euclid's Theorem Prime Number Theorem

2. This theorem, considered a fundamental theorem in mathematics, links two branches of calculus: differential calculus and integral calculus. This is known as the... Fundamental Theorem of Integration Fundamental Theorem of Differintegrals Fundamental Theorem of Differentiation Fundamental Theorem of Calculus

3. Limits - everyone's favourite! This rule/theorem uses derivatives to calculate limits of indeterminate forms (that of the form 0/0 or infinity/infinity). This is known as... L'Hôpital's Rule Cramer's Rule Cauchy's Mean Value Theorem Limit Rule

4. The indefinite integral of e^(x^2) is one of the many very special integrals. What makes it so special, in terms of numerical integration? Integration does not apply to exponentials with the base 'e' Numerical integration cannot be used for any integral with an exponent There is nothing special about it (numerical integration may be used) It cannot be integrated using elementary functions (numerical integraton)

5. Again, limits - my old friend. This theorem can be quite useful if you're not familiar with l'Hôpital's Rule. It states that if a function is bounded by two other functions and those two functions approach the same limit at a point, the function that is in between must also approach that very same limit. This is known as the... Ham Sandwich Theorem Squeeze, Pinching or Sandwich Theorem Pancake Theorem Hashbrown Theorem

6. Hyperbolic Functions - very interesting functions you learn about early in university calculus. One of the most famous applications of hyperbolic functions is to describe the shape of a hanging wire. The shape of the curve is given by the following equation: y = c + a cosh(x/a), where one can see the use of the hyperbolic function: cosh (hyperbolic cosine). What is the equation called? Bernoulli's Equation Hyperbolic Cosine Identity Equation Gaudí's Equation Catenary Equation

7. A very important thing to do, especially in mathematics, is to read your question(s) carefully. With that said, check out this integral: "the integral with limits from -1 to 1 of (1/x) dx." What, if anything, is wrong with this integral? The function has a discontinuity within the given limits The differential is missing Nothing is wrong with the integral - the answer is 0 The antiderivative of 1/x does not exist

8. In linear algebra, there is such a thing called mapping, using linear transformations. There are two properties that a transformation must hold in order to be linear: 1. Additivity: f(x + y) = f(x) + f(y) 2. Homogeneity: f(cx) = c f(x), where c is a constant An additional property (although sometimes not reliable) is that f(0) = 0. Knowing all this, which of the following transformations is linear? T(x,y,z) = (1,1) T(x,y) = (x + 1, y) T(x,y) = (2x + y, x - y) T(x,y,z) = (y^2, z)

9. When doing matrix row operations on a set of linear equations, you happen to get a row that looks like this: [0 0 0 ... 0 | x ], where x is any non-zero number You would classify this system as being... Linearly Dependent Consistent Inconsistent Linearly Independent

10. Here is an equation: (x,y,z) = (1,2,5) + t1(2,0,0) + t2(0,1,-2) What does this equation represent? A line passing through the point (1,2,5), parallel to the vectors (2,0,0) and (0,1,-2) A plane passing through the point (1,2,5), parallel to the vectors (2,0,0) and (0,1,-2) A plane passing through the points (2,0,0) and (0,1,-2), parellel to the vector (1,2,5) A line passing through the points (2,0,0) and (0,1,-2), parallel to the vector (1,2,5)