Approximate the area under the curve y = 1/(x−2) between x = 2 and x = 3 with six ordinates by:
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i) Trapezoidal rule
ii) Simpson rule
Find the value of k such that k(x² + y² ) + (y − 2x + 1)(y + 2x + 3) = 0 is a circle. Hence obtain the center and radius of the resulting circle.
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The circle x² + y² − 2x − 4y − 5 = 0 has a center C and is cut by the line y = 2x + 5 at A and B. Show that BC is perpendicular to AC and hence find the area of triangle ABC.
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Find the equation of the straight line which passes through the intersection of the lines 3x + 2y + 4 = 0 and x − y = 2 and forms the triangle with the axes whose area is 8 square units.
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Find the length of arc of the semi-cubical parabola y² = x³ between the points (1,1) and (4,8).
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If w = (z+2)/2 and |z| = 4, find the locus of the ‘w’
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Use the truth table to verify that the statement is a contradiction
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Use the laws of algebra of propositions to simplify the statement and hence draw the corresponding simple electrical network
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Without using the truth tables, prove that the proposition is tautolog
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Use vectors to prove the sine rule
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