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First of all key elements required for this question is the knowledge or retrival of these equations: tan2 + 1 =sec2 A tan(A-B) = (tanA-tanB)/(1+tanAtanB) so for the first equation...
To answer this we will need to use the product rule which is as follows: For y=uv, dy/dx=u'v+uv' where u' is the derivative of u and v' is the derivative...
Integrate by parts. First rewrite the integral in the form udv/dx, which is (1)ln(x). Then integrate (1)ln(x) wrt dx by assigning u=ln(x) du/dx=1/x and dv/dx=1 v=x. We can determine the integral of ln...
This is an example of completing the square.If we expand (x - p)^2 + q, we will have x^2 -2px + p + q.Now we can use algebra to work out what p and q are from the following equation. x^2 - 7x + 2 = x^2 -2...
Let the parabola be y=x2 and let the family of lines be y=2x+c, in order to study the intersection points we need to consider the second order linear system given by having the two equations ab...
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