1a. h=-4.9t^2+450 1b. h(t)=-4.9t^2+450 (h(2)-h(0))/(2-0) ((-4.9(〖2)〗^2+450)-(-4.9(0)^2+450))/2 =(430.4-450)/2 =-19.6 ∴The average velocity for the first two seconds was 19.6 metres per second. c. i) i) = =-24.5 ∴ The average velocity from is 24.5 metres/s. ii) = -14.7 iii) = -12.25 ∴ The average velocity from is 12.25 metres/s. d) Instantaneous velocity at 1s: =-9.8 ∴ The instantaneous velocity
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Sciences ECE / ICE / MexE Department ECE 352 VECTOR ANALYSIS DEL OPERATOR GROUP 3 Andaya‚ Rizalyn Ramos‚ Maria Issa P. ∇ Del is a symbol used in mathematics‚ in particular‚ in vector calculus‚ as a vector differential operator‚ usually represented by the nabla symbol ∇. Del may denote the gradient (locally steepest slope)‚ the divergence of a vector field‚ or the curl (rotation) of a vector field. The symbol ∇ can be interpreted as a vector of partial derivative operators‚ and its three
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Vector Analysis Definition A vector in n dimension is any set of n-components that transforms in the same manner as a displacement when you change coordinates Displacement is the model for the behavior of all vectors Roughly speaking: A vector is a quantity with both direction as well as magnitude. On the contrary‚ a scalar has no direction and remains unchanged when one changes the coordinates. Notation: Bold face A‚ in handwriting A . The magnitude of the vector is denoted by A A
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Calculus is the mathematical study of change‚[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches‚ differential calculus (concerning rates of change and slopes of curves)‚ and integral calculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental
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1. Gradient of a scalar field function Scalar Function: Generally‚ What Is Scalar Function? The Answer Is that a scalar function may be defined as A function of one or more variables whose range is one-dimensional‚ as compared to a vector function‚ whose range is three-dimensional (or‚ in general‚ -dimensional). Scalar Field When We Talk about Scalar Field‚ We Are Talking about the Scalar Function Being Applied to a Space (More like Euclenoid Space etc) or‚ a scalar field associates
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1. ht= -4.9t2+ 450‚ where t is the time elapsed in seconds and h is the height in metres. a) Table of Values t(s) | h(t) (m) | 0 | ht= -4.9(0)2+ 450= 450 | 1 | ht= -4.9(1)2+ 450= 445.1 | 2 | ht= -4.9(2)2+ 450= 430.4 | 3 | ht= -4.9(3)2+ 450= 405.9 | 4 | ht= -4.9(4)2+ 450=371.6 | 5 | ht= -4.9(5)2+ 450=327.5 | 6 | ht= -4.9(6)2+ 450= 273.6 | 7 | ht= -4.9(7)2+ 450= 209.9 | 8 | ht= -4.9(8)2+ 450= 136.4 | 9 | ht= -4.9(9)2+ 450=53.1 | 10 | ht= -4.9(10)2+ 450= -40 |
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History of Differential Calculus Universidad Iberoamericana September 20‚ 2013 Ever since men felt the need to count‚ the history of calculus begins‚ which together with Mathematics is one of the oldest and most useful science. Since men felt that need for counting objects‚ this need led to the creation of systems that allowed them to maintain control of their properties. They initially did it with the use of fingers‚ legs‚ or stones. But as humans continued developing
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How the calculus was invented? Calculus‚ historically known as infinitesimal calculus‚ is a mathematical discipline focused on limits‚ functions‚ derivatives‚ integrals‚ and infinite series. Ideas leading up to the notions of function‚ derivative‚ and integral were developed throughout the 17th century‚ but the decisive step was made by Isaac Newton and Gottfried Leibniz. Publication of Newton’s main treatises took many years‚ whereas Leibniz published first (Nova methodus‚ 1684) and the whole
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1. Calculus is split into two branches‚ differential calculus and integral calculus. Differential calculus is used to find the rates of change for geometric curves. This means that differential calculus is used to find the slope or tangent along a specific direction of a geometric curve. This relates directly to change‚ because finding the slope or tangent of a geometric curve is essentially finding the rate of change for that geometric curve. The other branch of calculus‚ integral calculus‚ is concerned
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History of Calculus Calculus is an integral part of the mathematics world. Various mathematicians coming from all parts of the world have shaped this theorem but the two main contributors are Sir Isaac Newton and Wilhelm Von Leibniz. The reason they are considered the inventors of Calculus is because they were able to give a unified approach to tangent and area problems unlike the others who used specific methods. Both of these mathematicians developed general concepts Newton was associated with
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