Search over 10,000 free study notes

Make use of identity sech^2(x) = tan^2(x) + 1 => 2{tan^2(x) + 1} = 3 + tan(x) Multiply out brackets and rearrange => 2tan^2(x) - tan(x) - 1 = 0 Use quadratic formula with a = 2, b = -1, c = -1 => ta...

If you have a differentiable function, stationary points are, by definition, those points where the derivative of the function is 0. Considering that the derivative of a function represents the rate of incre...

∫(8x3 + 4) dx = (8x^4)/4 + 4x + c= 2x^4 + 4x + c

We know that tan x =sin x/cos x, so we can multiply the whole equation by cos x which gives us => 2cos^2 x =3 sin x from the trig identity sin^2 (x)+ cos^2 (x)=1, we can sub in cos^2 (x)=1-sin^2(x) => ...

Test factors of -3 to find a root for the equation. For example, try 1, 1^3+3*1^2-1-3=0, so 1 is a root, and (x-1) is a factor. Now it's known that: (ax^2+bx+c)(x-1)=x^3+3x^2-x-3. By comparing coefficients f...