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Firstly I would state the rule that for any composite function fg, its domain is always the domain of g. If the student would like to know why this is the case, I would simplify the expression fg(x) to f(...

We start off by differentiating the equation implicitly which will give us:2(x-y) -2(x-y)dy/dx = 6 + 5dy/dxThen we rearrange to get dy/dx on it's own:dy/dx = (2x-2y-6)/(2x-2y+5)
For the second part o...

The equation for a circle is pi x radius x radius. So,first we need to find the radius which is half the diameter, 140 divided by 2 equals 70 cm. As the question asks for the answer as a multiple of pi th...

To solve this question, we have to use substitution. We substitute the line equation,y=x+1, into the circle equation so that we get, x^2 + (x+1-1)^2=18. This reduces to 2x^2 = 18, then dividing both sides...

Using integration by parts by letting u=x and dv/dx=e^-x. this implies that du/dx=1 and v=-e^-xThe By Parts formulae is u.v - integral(v.du/dx) = -xe^-x - in...