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(In terms of formatting, we'll use y' to represent dy/dx, exp() to represent the expoential e^(), int() to represent integration with respect to x, and 1ODE to mean First-Order Ordinary Differential Equat...

First we need to find the critical values. To find the critical values we must rearrange the equation and then replace the inequality symbol with an equals sign. The ≤ can be treated as an equality as lon...

Newton-Raphson is used for finding a numerical solution to equations of the form f(x)=0. The question asks for the square root of 3, which algebraically looks like this: x = sqrt(3) This can be rewritten ...

Complex numbers have three primary forms: the general form, z=a+ib; the polar form, z=r(cosθ+isinθ); and the exponential form, z=rexp(iθ). To convert from the general form to either form you need to find ...

x=5 is a solution, so (x-5) is a factor of f(x). So, to find the other solutions, factorise f(x): f(x)=(x-5)(ax^2+bx+c). We know it will be of this form because f(x) is cubic. To find the values of a, b a...