Mean value theorem and Rolle’s theorem ( solutions)īack to 100-level mathematics revision Exercises. Application of differential calculus.pdf - Chapter 20 Applications of differential calculus Syllabus reference: 6.2, 6.3, Application of differential calculus.pdf - Chapter 20.Optimisation problems: Two ( solutions).Optimisation problems: One ( solutions).Differentiating inverse trig functions ( solutions).Implicit differentiation: Extension ( solutions).Implicit differentiation: Four ( solutions).Implicit differentiation: Three ( solutions).
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Implicit differentiation: One ( solutions) For demonstrations of how to apply differential calculus in optimisation problems such as maximising or minimising functions over an interval.Worksheets 16 and 17 are taught in MATH109. Applications of calculus For demonstrations of how to use the concepts and tools of differential calculus to sketch graphs and curves of functions through several worked examples. Worksheets 1 to 15 are topics that are taught in MATH108. These revision exercises will help you practise the procedures involved in differentiating functions and solving problems involving applications of differentiation. A Mars-sized body can be found at not less than 70–85 au: such bounds are 147–175 au, 1006–1200 au, 4334–5170 au, 8113–9524 au and 10 222–12 000 au for a body with a mass equal to that of the Earth, Jupiter, a brown dwarf, red dwarf and the Sun, respectively.100-level Mathematics Revision Exercises Differentiation and Applications We also determine the forbidden spatial region for X by plotting its boundary surface in the three-dimensional space it shows significant departures from spherical symmetry. For each of them we plot rmin X as a function of the heliocentric latitude β and longitude λ. To constrain rX we consider the case of a rock-ice planet with the mass of Mars and the Earth, a giant planet with the mass of Jupiter, a brown dwarf with MX = 80mJupiter, a red dwarf with M = 0.5M and a Sun-mass body. As a result, we find that Mars yields the tightest constraints, with the tidal parameter KX = GMX/r3X ≤ 3 × 10−24 s−2. We show that the indirect effects of X on the inner planets through its action on the outer ones can be neglected, given the present-day level of accuracy in knowing ˙. tion for all further study and application of mathematics and statistics, presenting an introduction to dierential calculus, integral calculus, algebra, dierential equa-tions and statistics, providing sound mathematical foundations for further studies not only in mathematics and statistics, but also in the natural and social sciences. The perihelion precessions induced by them can be analyticallyworked out only for some particular positions ofXin the sky in general, numerical calculations are used.
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The direct action of X on the inner planets can be approximated by a elastic Hooke-type radial acceleration plus a term of comparable magnitude having a fixed direction in space pointing towards X.
Pitjeva by fitting a huge planetary data set with the dynamical models of the EPM ephemerides, to put constraints on the position of a putative, yet undiscovered large body X of mass MX, not modelled in the EPM software. "We use the corrections ˙ to the standard Newtonian/Einsteinian perihelion precessions of the inner planets of the Solar system, recently estimated by E.V.
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