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We are presented with a third order polynomial with 4 terms, so we expect 3 solutions for f(x)=0. To prove that (x-2) is a factor we must insert the value of x=2 into the function and if f(2)=0 then we ha...

L = (H²+R²)^1/2 V = (1/3)πR²(H²+R²)^1/2

dV/dt = -k

dH/dt = dH/dV × dv/dt

dV/dH = (1/3)πR²H(H^...

∫ln(x)dx = xln(x) - ∫x/x dx = xln(x) - x + C

Any constant (say k) can be rewritten as kx⁰ since x⁰=1. When you differentiate this, the 0 which is the power of the x term gets dragged to the front and is multiplied with the rest...

When finding the maximum or minimum of an equation, make sure you rearrange an equation to make y the subject of the equation i.e. y=_________. You can then differentiate with respect to x and then set th...