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x = sinhy=> dx/dy = coshycosh²y - sinh²y = 1=> sqrt(1 + sinh²y) = coshythus dx/dy = sqrt(1 + sinh²y)and dy/dx = 1/sqrt(1 + sinh²y)hence dy/dx =...

All coefficients of z are real, therefore one root must be the complex conjugate so β = 1-3i.It is known that Σαβ = 18 (the coefficient of z), so we can get an equation in the third root, γ, as follows: Σ...

Use the identity sin^2(y) + cos^2(y) = 1 to get the expression sin^2(3x) (1-sin^2(3x)) cos(3x) dx.Use the substitution u= sin(3x) by dividing the expression by the derivative, u’= 3cos(3x).The expression ...

The first thing you should do is Plan. You need to think about what points you will make, the responses and counter-responses you will discuss and how you will conclude.This is the best way to make sure y...

Firstly we can use the fact that cosx is the real part of e^ix. This means that the series above is the real part of the infinite series 1 + 1/2e^ix + 1/4e^2ix + ...... This means that we have an infinite...