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Euler's Formula is: e ix = cos(x) + isin(x) This identity comes from the Maclaurin expansion of the exponential function. The resulting maclaurin series is a power series in x with odd terms having a factor ...

It is possible to solve this question using integration by parts. However, we note that sin(x) is an odd function, meaning that sin(-x) = -sin(x). Thus x 2 sin(x) is also an odd function. This means that the...

To begin with, we should find the equation of the line. To do this we appoint a position vector and a direction vector. The position vector can simply be one of the two points we are give, i.e. (6,4,1). To f...

divide through by 2x to get: dy/dx + 2y/x = 4x this is now in the form of dy/dx + P(x)y = Q(x) intergrating factor = exp( integral(P(x)) dx ) = exp( integral(2/x) dx ) = exp( 2 ln(x) ) = x 2 therefore d( (x ...

Write y = sinh^(-1)(x) ie x = sinhy. Then writing this in terms of exponentials and multiplying by 2 we will get 2x = exp(y) - exp(-y). Multiply by exp(y) and rearrange to obtain exp(2y) - 2xexp(y) -1 = 0. T...