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These are simultaneous equations and we need to find the value of X and Y. We can use the elimination method. The coefficients (the amount the letter is being multiplied by) of X and Y do not match. First...

To find an extreme point of a function you must first take the derivative of f(x) with respect to x.
As the function will peak/trough at the extreme point, the gradient at this point will be equal to...

(a)To find the turning points of a curve, need to solve dy/dx=0. Using the quotient rule one can differentiate y:y=f(x)/g(x) dy/dx=(f'(x)g(x)-f(x)g'(x))/(g(x))²f(x)=3x, f'(x)=3, g(x)=(9+x^2...

Try differentiating:sin(x)cos(z-x)+cos(x)sin(z-x)with respect to x and for constant z, then simply the derivative you deduce, then integrate throughout the simplified equation. See what happens!

There are two definitions of the sine and cosine functions that anyone who uses contemporary maths, and I do mean anyone, uses silently or otherwise. The first is as follows:'Rotate the point (1,0) in Euc...