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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...
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
What you would do in this scenario is consider all the terms in the expression you are integrating. You then want to go through the acronym LATE to choose which term you should differentiate.L stands for ...
Integrating sin^2A and cos^2A is a bit nasty so we can use double angle formula to make it a little simpler. cos2A = cos^2A - sin^2A = 2cos^2A - 1. We can rearrange to get cos^2A in nicer terms. cos^2A = ...
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