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Math 141
Math 141

... Therefore, in order to maximize the amount of light to enter our window would have be constructed in the shape of a rectangle approximately 5.6 x 2.8 and the semicircular part would have a radius of approximately 2.8. 5. What is the maximum volume for a rectangular box (square base, no top) made fro ...
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Graph Sketcher Suggestions

... Choose the list of x values (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 might be a good list) and then calculate the corresponding y values. Use this chart to fill in the points to be plotted in simpleplot. To do the explorations below, be sure to calculate many points (10 or more). Exploration 1: Up and ...
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... Here σ(N) represents the familiar divisor function of number theory. We first came up with this quotient a little over a year ago(see http://www2.mae.ufl.edu/~uhk/NUMBERFRACTION.pdf ) and have explored its properties at length since that time. We term f(N) for any given N the Number Fraction. If one ...
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I. Precisely complete the following definitions: 1. A natural number n
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Computer Science 341 Discrete Mathematics Homework 4
Computer Science 341 Discrete Mathematics Homework 4

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ON ABUNDANT-LIKE NUMBERS

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... ­the total cost C for p pounds of copper if each pound costs $3.57 ­the height in feet, f, of an object when you know the objects  height h in inches Write a rule AND evaluate: ­A kennel charges $15 per day to board dogs.  All dogs have to  get a flea bath for $12.  Write a rule for total cost n day ...
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Homework 1 Solutions - UCSD Math Department

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... Recall that functions such as f(x) = x1/2 and f(x) = log x are not continuous on all real numbers, nevertheless, they are continuous at every number in their domains. For example, the domain of f(x) = x1/2 is [0, ) and its interval of continuity is also [0, ). Similarly, the domain of f(x) = log x ...
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... Finding the Area Between the Graphs of f (x) and g(x) 1. Find all points of intersection by solving f (x) = g(x) for x. This either determines the interval over which you will integrate or breaks up a given interval into regions between the intersection points. 2. Determine the area of each region y ...
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... A linear function that fits the data is S(x) = ? (Let x = the number of years since 1990, and let S = the average salary x years from 1990.) ___________________________________________________________________ (a) Let the linear function be y = mx + b, where x = the number of years after 1991 [Thus, ...
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... (d) Let v1 and v2 be the bases for E 1 and E 2 , respectively. Then B = {v1 , v2 } is a basis for R2 . Use this basis to diagonalize A; that is, write A = SDS 1 for some matrix S and some diagonal matrix D. (Hint: All the heavy lifting has been done in the previous parts of this problem.) (e) Use pa ...
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... 1. Solve the system of linear congruence’s: x  2(mod3) , x  3(mod5) and x  1(mod7) . 2. Prove that there exists infinite number of prime integers. 3. (a) Suppose there are eight teachers in the BEC and their coded identification numbers 2733, 1396, 2724, 1522, 1952, 2088, 2155, 1850. Create a fi ...
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MATH 1830 Section 5

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Unit 5 Test Name: Part 2 (Exponential Functions) Block: ______ A

... a. The range is the set of all real numbers less than 0. b. The domain is the set of all real numbers greater than -4. c. The range is the set of all real numbers greater than 0. d. The domain is the set of all real numbers less than -4. ...
2011 GHSGT Math Practice Questions
2011 GHSGT Math Practice Questions

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Non-standard calculus

In mathematics, non-standard calculus is the modern application of infinitesimals, in the sense of non-standard analysis, to differential and integral calculus. It provides a rigorous justification for some arguments in calculus that were previously considered merely heuristic.Calculations with infinitesimals were widely used before Karl Weierstrass sought to replace them with the (ε, δ)-definition of limit starting in the 1870s. (See history of calculus.) For almost one hundred years thereafter, mathematicians like Richard Courant viewed infinitesimals as being naive and vague or meaningless.Contrary to such views, Abraham Robinson showed in 1960 that infinitesimals are precise, clear, and meaningful, building upon work by Edwin Hewitt and Jerzy Łoś. According to Jerome Keisler, ""Robinson solved a three hundred year old problem by giving a precise treatment of infinitesimals. Robinson's achievement will probably rank as one of the major mathematical advances of the twentieth century.""
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