tool for describing the real world in mathematical terms. A function can be represented by an equation‚ a graph‚ a numerical table or a verbal description. In this section we are going to get familiar with functions and function notation. MAT133 Calculus with Analytic Geometry II Page 1 An equation is a function if for any x in the domain of the equation‚ the equation yields exactly one value of y. The set of values that the independent variable is allowed to assume‚ i.e.‚ all possible
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After choosing a topic randomly‚ students will have 5 minutes to prepare before presenting their explanation for 5 minutes. 1. State the definition of the limit and explain the requirements for a limit to exist. Also‚ explain the 3 main techniques to evaluate limits. (Keywords: limit‚ intend‚ left‚ right‚ general‚ notation‚ 3 requirements‚ NAG‚ table‚ diagrams‚ indeterminate form‚ conjugate‚ factoring‚ substitution) The limit of the function is the height that the function intends to reach
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Calculus I. What is Calculus? Calculus is the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions‚ by methods originally based on the summation of infinitesimal differences. a. Differential Calculus - concerned with the determination‚ properties‚ and application of derivatives and differentials. b. Integral Calculus - concerned with the determination‚ properties‚ and application of integrals. II. Brief History of Calculus Calculus was
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prominent figure in mathematics and was a major mathematician that greatly contributed to calculus. Leibniz’s contribution to the invention of infinitesimal calculus was monumental and is widely recognized as modern mathematics starting point. Leibniz’s Nova Methodus pro Maximis et Minimis‚ itemque Tangentibus… in Acta Eruditorum‚ in 1684‚ published Leibniz’s details of his ideas of differential calculus. The paper contained the d notation‚ the derivatives of powers rule‚ the quotient rule‚ and
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Calculus Reaction Paper “Teaching Real Analysis in the Land of Make Believe” The article of Teaching Real Analysis in the Land of Make Believe is a very nice article. It had made learning Calculus simple because it is stated in a child friendly way. Instead of using long and difficult equations and definitions‚ it is stated through a form of a tale. The author used the different symbols in calculus as its characters. This made the students more interested in the field of calculus. They
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AP Calculus Name ____________________________ Period _____ Functions Defined by Integrals The graph below is‚ the derivative of. The graph consists of two semicircles and one line segment. Horizontal tangents are located at and and a vertical tangent is located at. 1. On what interval is increasing? Justify your answer. 2. For what values of x does have a relative minimum? Justify. 3. On what intervals is concave up? Justify 4. For what values of x is undefined? 5. Identify
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create symbolic math expressions. This is useful when you don’t want to immediately compute an answer‚ or when you have a math "formula" to work on but don’t know how to "process" it. Matlab allows symbolic operations several areas including: * Calculus * Linear Algebra * Algebraic and Differential Equations * Transforms (Fourier‚ Laplace‚ etc) The key function in Matlab to create a symbolic representation of data is: sym() or syms if you have multiple symbols to make. Below is an
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Academy of Sciences in 1731‚Euler married Katharina Gesell x (Wikipedia‚2012). The couple had five children who survived childhood out of thirteen x (Wikipedia‚ 2012). Euler worked in nearly every area of mathematics including geometry‚ infinitesimal calculus‚ trigonometry‚ algebra‚ and number theory‚ as well as continuum physics‚ and the lunar theory(Wikipedia‚2012). He introduced the concept of a
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n calculus‚ Rolle’s theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero. ------------------------------------------------- Standard version of the theorem [edit] If a real-valued function f is continuous on a closed interval [a‚ b]‚ differentiable on the open interval (a‚ b)‚ and f(a) = f(b)‚ then there
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Conjugate-beam method • Superposition method • Virtual work method Double Integration Method The edge view of the neutral surface of a deflected beam is called the elastic curve 1 M ( x) EI ρ Double Integration Method • From elementary calculus‚ simplified for beam parameters‚ d2y 2 2 1 d y dx 2 2 3 2 dx dy 1 dx • Substituting and integrating‚ 1 d2y EI EI 2 M x dx x dy EI EI M x dx C1 dx 0 x x EI y dx M x dx C1x C2 0
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