Mathematics - About Krypton
... If a and b are the lengths of the two short sides of a right triangle and c is its long side then this formula holds. Conversely, if the formula holds then a triangle whose sides have length a, b and c is a right triangle. This formula is about 2,350 years old and due to Pythagoras of Samos. It is u ...
... If a and b are the lengths of the two short sides of a right triangle and c is its long side then this formula holds. Conversely, if the formula holds then a triangle whose sides have length a, b and c is a right triangle. This formula is about 2,350 years old and due to Pythagoras of Samos. It is u ...
MI4 PS06 - F16
... 8) Suppose that an isosceles triangle has two sides of length a and one side of length c. a. Find the area of the triangle in terms of a and c. Simplify as much as you can. b. A well-known formula for the area of a triangle is called Hero’s Formula. It is given by ...
... 8) Suppose that an isosceles triangle has two sides of length a and one side of length c. a. Find the area of the triangle in terms of a and c. Simplify as much as you can. b. A well-known formula for the area of a triangle is called Hero’s Formula. It is given by ...
The Mean Value Theorem Math 120 Calculus I
... Warning: The second-derivative test is inconclusive when f 00 (x0 ) = 0. If that happens use the first-derivative test. (Yes, you could look at the third derivative, but we won’t go there.) Concavity and the second derivative. There are three equivalent conditions for a differentiable function to b ...
... Warning: The second-derivative test is inconclusive when f 00 (x0 ) = 0. If that happens use the first-derivative test. (Yes, you could look at the third derivative, but we won’t go there.) Concavity and the second derivative. There are three equivalent conditions for a differentiable function to b ...
9 Complex-valued Functions
... Ascoli-Arzela Theorem It is known (see Theorem 9.1) that any bounded sequence of real (or complex) numbers has a convergent subsequence. In the theory of functions, one may ask a similar question: For a sequence of bounded continuous functions, is there any uniformly convergent subsequence (so that ...
... Ascoli-Arzela Theorem It is known (see Theorem 9.1) that any bounded sequence of real (or complex) numbers has a convergent subsequence. In the theory of functions, one may ask a similar question: For a sequence of bounded continuous functions, is there any uniformly convergent subsequence (so that ...
AP CALCULUS AB FREE-RESPONSE QUESTIONS (review #10)
... 1. (2002 exam, #1) Calculators allowed Let f and g be the functions given by f ( x) e x and g ( x) ln x . (a) Find the area of the region enclosed by the graphs of f and g between x ...
... 1. (2002 exam, #1) Calculators allowed Let f and g be the functions given by f ( x) e x and g ( x) ln x . (a) Find the area of the region enclosed by the graphs of f and g between x ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.