7.5 The Converse of the Pythagorean Theorem
... equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. 8. G.6 Explain a proof of the Pythagorean Theorem and its converse. 8. G.7 Apply the Pythagorean Theorem t ...
... equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. 8. G.6 Explain a proof of the Pythagorean Theorem and its converse. 8. G.7 Apply the Pythagorean Theorem t ...
Document
... Functions are often denoted by letters such as f, F, g, G, and others. The symbol f(x), read “f of x” or “f at x”, is the number that results when x is given and the function f is applied. Elements of the domain, x, can be though of as input and the result obtained when the function is applied can ...
... Functions are often denoted by letters such as f, F, g, G, and others. The symbol f(x), read “f of x” or “f at x”, is the number that results when x is given and the function f is applied. Elements of the domain, x, can be though of as input and the result obtained when the function is applied can ...
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Section 1.1: Four Ways to Represent a Function
... Section 1.1: Four Ways to Represent a Function 1. The Definition of a Function Functions are one of the most basic tools in mathematics, so we start by considering the definition of a function and all related concepts. Definition 1.1. A function f is a rule which assigns to each element in a set D, ...
... Section 1.1: Four Ways to Represent a Function 1. The Definition of a Function Functions are one of the most basic tools in mathematics, so we start by considering the definition of a function and all related concepts. Definition 1.1. A function f is a rule which assigns to each element in a set D, ...
chapter1
... We can combine functions in any of five ways. Four of these are the familiar arithmetic operations; addition, subtraction, multiplication and division, and are very intuitive. The fifth type of combining functions is called composition of functions. In all cases, we’ll be interested in combining the ...
... We can combine functions in any of five ways. Four of these are the familiar arithmetic operations; addition, subtraction, multiplication and division, and are very intuitive. The fifth type of combining functions is called composition of functions. In all cases, we’ll be interested in combining the ...
Calculus II
... series for |x| and convergent geometric series with r = ¯ c ¯. ¤ From this theorem we could conclude that P Theorem 9.6.3 If bn xn is a power series, then exactly one of the following true: (i). The series converges only if x = 0. (ii). The series is absolutely convergent for every x. (iii). There i ...
... series for |x| and convergent geometric series with r = ¯ c ¯. ¤ From this theorem we could conclude that P Theorem 9.6.3 If bn xn is a power series, then exactly one of the following true: (i). The series converges only if x = 0. (ii). The series is absolutely convergent for every x. (iii). There i ...
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.