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In this sequence, there is no common difference between one term and the next making it more challenging to solve. However, if you look at the terms closely, you can see that each term is the sum of the p...
Question is asking for gradient at x = 0, y = ln2. e^2y = 5 - e^-x. Differentiation with respect to x: 2e^2y * dy/dx = e^-x . dy/dx = e^-x / 2e^2y. At x = 0, y = ln2 ~ dy/dx = e^0 / 2e^2ln2 = 1 / 2e^ln4 =...
1a) 1000/7=142.8.... Therefore there are 142 multiples of 7 between 1 and 1000 Therefore the sum of series from 1 to 142 is 1/7th of the solutionCalculation:70.5142143=71071...
From x : y = 7 : 4 work out an expression for x: x = y (7/4) and substitute into x + y = 88: y(7/4 + 1) = 88y( 11/4) = 88 y = 88 (4/11) = 8 x 4 = 24substitute this into x + y = 88 to get x = 88 - 24 = 64....
sin^2(x) = (1 - cos(2x))/2 and cos^2(x) = (1 + cos(2x))/2so sin^4(x) = 0.25(1 - 2cos(2x) + cos^2(2x)) = 0.25(1 - 2cos(2x) + 0.5 + 0.5cos(4x))integrate = 3x/8 - sin(2x)/4 + sin(4x)/32
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