SECTION 2.3 If f : X → Y is a function, we say that X is the domain
... Domain = N becuase it takes nonnegative integers as input. The Range is the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, assuming we are counting numbers in base 10. b.) The function that assigns the next largest integer to a positive integer. Domain = N − {0} = {1, 2, 3, 4, . . .}. The range is N − {0, 1} = ...
... Domain = N becuase it takes nonnegative integers as input. The Range is the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, assuming we are counting numbers in base 10. b.) The function that assigns the next largest integer to a positive integer. Domain = N − {0} = {1, 2, 3, 4, . . .}. The range is N − {0, 1} = ...
On the number e, its irrationality, and factorials
... number of times. Therefore there can be no integers a and b for which 2 = a/b. All proofs that a number r is irrational follow this pattern of logic, called proof by contradiction: To prove that r is irrational we assume r = a/b for some integers a and b and then show (somehow) that this assumption ...
... number of times. Therefore there can be no integers a and b for which 2 = a/b. All proofs that a number r is irrational follow this pattern of logic, called proof by contradiction: To prove that r is irrational we assume r = a/b for some integers a and b and then show (somehow) that this assumption ...
Recitation Note 1 Some Integration Theorem
... The integral of v with respect to u is equal to uv minus the integration of u with respect to v. ...
... The integral of v with respect to u is equal to uv minus the integration of u with respect to v. ...
Section 4.1
... Guidelines for Determining the Domain: The domain of all linear functions is the set of all real numbers, . If there is a variable in the denominator, the domain cannot contain any value that makes the denominator equal to zero. If there is a variable under a square root symbol, the domain ca ...
... Guidelines for Determining the Domain: The domain of all linear functions is the set of all real numbers, . If there is a variable in the denominator, the domain cannot contain any value that makes the denominator equal to zero. If there is a variable under a square root symbol, the domain ca ...
4.6 Formalizing Relations and Functions
... f is not a variable, but the name of the function. Used to show that the function value depends on the independent variable, the value of x. ...
... f is not a variable, but the name of the function. Used to show that the function value depends on the independent variable, the value of x. ...
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The Fundamental Theorem of Calculus [1]
... which can be interpreted as the area under the graph of f from a to x, and the blue part in Figure 1. Here in the graph f happens to be a positive function. To compute g ′ (x), let’s use the definition of a derivative. For h > 0, g(x + h) − g(x) is obtained by subtracting areas, so it is the area un ...
... which can be interpreted as the area under the graph of f from a to x, and the blue part in Figure 1. Here in the graph f happens to be a positive function. To compute g ′ (x), let’s use the definition of a derivative. For h > 0, g(x + h) − g(x) is obtained by subtracting areas, so it is the area un ...
Fundamental Theorem of Calculus, Riemann Sums, Substitution
... Notice that the integral involves one of the terms above. Substitute the appropriate u. Make sure to change the dx to a du (with relevant factor). Simplify the integral using the appropriate trig identity. Rewrite the new integral in terms of the original non-Ѳ variable (draw a reference right-trian ...
... Notice that the integral involves one of the terms above. Substitute the appropriate u. Make sure to change the dx to a du (with relevant factor). Simplify the integral using the appropriate trig identity. Rewrite the new integral in terms of the original non-Ѳ variable (draw a reference right-trian ...
Lesson 18 – Finding Indefinite and Definite Integrals 1 Math 1314
... indicates that the indefinite integral of f (x) with respect to the variable x is F ( x) C where F (x) is an antiderivative of f. The reason for “+ C” is illustrated below: Each function that follows is an antiderivative of 10x since the derivative of each is 10x . F ( x) 5 x 2 1 , G ( x) 5 ...
... indicates that the indefinite integral of f (x) with respect to the variable x is F ( x) C where F (x) is an antiderivative of f. The reason for “+ C” is illustrated below: Each function that follows is an antiderivative of 10x since the derivative of each is 10x . F ( x) 5 x 2 1 , G ( x) 5 ...
Math 1100 Practice Exam 3 23 November, 2011
... 1. Be able to define/explain/identify in a picture/draw the following (a) Definite integral (b) Indefinite integral (c) Average value of a function (d) Fundamental Theorem of Calculus ...
... 1. Be able to define/explain/identify in a picture/draw the following (a) Definite integral (b) Indefinite integral (c) Average value of a function (d) Fundamental Theorem of Calculus ...
