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First, write the line in vector form r=(1 1 1) + t(1 2 -1). Consider a point P on the line such that the line connecting P and A is perpendicular to L. The vector P->A is (2 3 4) - (1 1 1) - ...

This is an algebraic fraction. There is more than one way of solving this expression, but the simplest is to factorise both the top and the bottom quadratic expressions.Firstly we shall simplify the top e...

A simple way to differentiate an equation with respect to x is to reduce each x components power by one and multiply each x component by their original power.

Looking at the equation y = ...

A good approach to solve this is to use the chain rule of differentiation. The chain rule states: dy/dx= (dy/du)*(du/dx).

In this case let u = 1+3x, so y = u^2.

Then dy/du =...

Here we need to use the chain rule because we have a function (natural log) of another function (x^2+3x+5). Let u=x^2+3x+5, and differentiate lnu with respect to u, this gives us 1/u. Then we different...