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Where the graph intersects the x-axis, x²+2kx+5 must be equal to zero. Thus we can answer the equivalent question: For what k does x²+2kx+5 = 0 not have a solution?This is now a simp...

When you see a complicated product, split it into the form u.v', where u and v' are algebraic expressions such as x^2. You can then use the formula: uv'=uv-integral(vu') which you would take between an...

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We begin solving this problem by finding the gradient of the tangent line at H, which is equal to dy/dx.

In this case, our curve has equations  x = 3sinθ and ...

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When asked to exrpess something in partial fractions, we first compare the power of the numerator to the power of the denominator.

In our case we have that th...

When thinking about stationary points, it is important to remember that these points happen when the gradient of the curve is 0 (-> dy/dx = 0), or if you prefer, when the rate of change of a graph is 0...