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for each of the terms in x, the power to which x is raised increases by 1, and then each term is divided by the new power. A constant of integration is introduced because we were not asked to integrate betwe...

Each vector line can be simplified into three separate equations in terms of the lines parameter and one of 'x,y and z.' This process can be done for both lines, creating six equations in total. By setting t...

Take the integral as 1 x ln(x) instead of just ln(x). Use integration by parts giving two terms, the first is now just xln(x) and the second is the integral of 1 dx. This is easy to integrate giving the fina...

So, basically |z| = 1 is equal to the set containing all complex numbers where their magnitude is equal to one. Also, by unraveling the definition of |z| we get that (x 2 +y 2 ) 1/2 =1 which is the same as x...

The answer to this question is in two parts. We firstly must find the derivative of the function y=f(x) with respect to x, and then substitute the value of x given in the question to find the gradient at tha...