Top answers

How do you prove two straight lines intersect?

There are two ways to prove they intercept (you can choose whichever one you prefer). Say we have two straight lines, for example: r 1 = 3 i + 4 j - 5 k + t ( i - 2 j + 2 k ) => r 1 = (3 + t) i + (4 – 2t)...
NM
Answered by Nicholas M. • Maths tutor
11780 Views

Given that y = x^4 tan(2x), find dy/dx

Here we have a product of two functions - they are being multiplied together - so we need to use the product rule. The product rule is: if y = u·v, dy/dx = v·u' + u·v' (where f' stands for df/dx). u = x^4 du...
DB
Answered by Douglas B. • Maths tutor
10832 Views

Find the first four terms in the binomial expansion of (2 + x) ^5

Firstly we must take the 2 out of the bracket, as a binomial expansion must have a coefficent of 1 (2 + x) 5 = 2 5 (1 + 0.5x) 5 Then, it is a good idea to quote the binomial expasion formula (you can often p...
FO
Answered by Fiona O. • Maths tutor
20024 Views

Find and classify all the stationary points of the function f(x) = x^3 - 3x^2 + 8

Stationary points occur when the gradient of the function is zero. They can be visualised on a graph as hills (maximum points), as troughs (minimum points), or as points of inflection. (I would draw all thre...
RB
Answered by Ryan B. • Maths tutor
13674 Views

Differentiate y = (sin(x))^2 (find dy/dx)

This a relatively simple question which requires the use of the chain rule to solve. First we set u = sin(x) so we then have y = u 2 . Next we perform do differentiations, one on u as a function of x and the...
TC
Answered by Tabraiz C. • Maths tutor
18655 Views