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When dealing with a linear and quadratic simultaneous equation, it is best to use subsitution to approach it.I take the linear equation and put it in terms of one variable. In this case, to avoid fraction...

Differentiate the equation.Let the derivative equal to 0 and get x.Substitute the value of x into the original equation to get y.

a) 54-45+3a+18=0 3a+27=0 3a=-27 and thus a=-9b) 2x^3 – 5x^2 -9x + 18 = (x-3) (2x^2 +bx-6)to find b ; collect the x^2 terms so bx^2-6x^2=-5x^2 and thus b=1c) when comparing f(y) and f(x) we see ...

e^{x^2} --------> dy/dx = 2xe^{x^2}

use the formula integral(uv') = uv - integral(vu') so the tricky integral can be avoided (this formula can be derived from integrating the product rule) so in these questions all you need to ...