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Showing 191 - 200 of 297 results for "The wave"
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https://sheffield.ac.uk/media/31990/download?attachmentd) Show that the position vector r and velocity vector ṙ are perpendicular. ... Thisresult generalizes in an obvious way to three dimensions as summarized in the following Key Point. ... complicated expressions involving vectors provided certain...
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https://sheffield.ac.uk/media/31991/download?attachmentThe standardrepresentations for a.c. electronic signals are. v = V0ejωt and i = I0e. ... The constant of proportionality (capacitance) is given the symbol C. So q = Cv. ... 1. (1 ω2LC jωRC). (b) Multiplying by the complex conjugate of the...
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https://sheffield.ac.uk/media/31995/download?attachmentPrerequisites. Before starting this Section you should. • thoroughly understand the various techniquesof differentiation. '. &. ... below. You could check the entries in this table usingyour knowledge of differentiation. ... Task. Find. e2x dx...
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https://sheffield.ac.uk/media/31996/download?attachmentPrerequisites. Before starting this Section you should. • understand integration as the reverse ofdifferentiation. • ... 3= 21. Example 10Find the definite integral of cos x from 0 to. ... Consider a small element x of the extension beyond an...
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https://sheffield.ac.uk/media/31999/download?attachmentThetechnique is illustrated in the following Example. Example 19. Find. (3x 5)6dx. ... suitable. Consider the next Example. Example 22Find the indefinite integral. x2. x3 1dx. ... Solution. First look at the function we are trying to integrate: (3x...
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https://sheffield.ac.uk/media/32003/download?attachmentof solids formed when curves are rotated around the x or y axis. ... Write down the expression which represents summing the volumes of all such discs:. ... 0. πx4 dx. Perform the integration to find the volume of the solid:. ... The radius of a...
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https://sheffield.ac.uk/media/32012/download?attachmentthe series converges absolutely if |x| < R. • the series diverges if |x| > R. • ... 1 x. 3+. x2. 32+. x3. 33+. First find the coefficient of xp:. ... We. know, from the ratio test that. p=0. bpxp is absolutely convergent if. ... which is...
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https://sheffield.ac.uk/media/32007/download?attachmentThe figure above shows the disc lying in the plane of the paper. ... This is (2πrρδr) r2 = 2πr3ρδr. The contribution from all rings must be summed. ... mass of the body the square of the distance between the two axes. ... These are...
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https://sheffield.ac.uk/media/32020/download?attachmentf. x= 3x2 16x 2. Now if we return to the original formulation. ... we havedone for the x-variable we can do for the y-variable. ... the partial derivative of f with respect. to v (say) is denoted byf. ... y. (f. x. ). For the function in Example 7f....
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https://sheffield.ac.uk/media/32022/download?attachmentThe absolute error in f is δf. The relative error in f isδf. ... Example 12Estimate the absolute error for the function f(x, y) = x2 x3y. ... We see that there is a reasonably close correspondence between the two values. ... in the value of the...