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Starting with a(x - b)^2 - c, if we expand the bracket we get:

a(x^2 - 2xb + b^2) -c

Since we need to end up with the coefficient on x^2 being 3 and in the expression above x^2 is only multi...

|Z| = sqrt(1/2^2 + (sqrt(3)/2)^2) = 1 arg(Z) = arctan((sqrt(3)/2)/(1/2)) = pi/3 Z = cos(pi/3) + jsin(pi/3) Z = e^j(pi/3) Apologies for the use of sqrt(), I have no way yet of using the symbol on my laptop...

First we must differentiate the equation with respect to x. To differentiate you must multiply the coefficient (number in front) by the power of x, then subtract 1 from the power. So here we find dy/dx = ...

3x² + 2x + 4

Starting with ∫a^x dx ,
We can re-write a^x using logs as e^ln(a)*x using some of their properties
We use the substitution u = ln(a)*x (as such du/dx = ln(a)) all...