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How do I show two lines are skew?

Skew lines in 3 dimensions are those which are not parallel and do not intersect. Let's take two example lines: l 1 = (2, 2, -1) + λ(3, 1, -3) and l 2 = (1, 0, 1) + µ(6, -4, 9) First we need to show that the...
DM
Answered by David M. • Maths tutor
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Find the tangent of the following curve, y=xe^x, at x=1 expressing it in the form y=mx+c?

Firstly, we calculate the y-value when x=1, namely y=e. Then we need to find the gradient of this curve at x=1, which can be determined by taking the derivative of y and then valuate it at x=1. So dy/dx=xe^x...
BS
Answered by Bruno S. • Maths tutor
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given y=(1+x)^2, find dy/dx

There are two ways in which this we can do this, The first is explanding the brackets to get 1+2x+x 2 and differentiating to get 2+2x. The second way is using the chain rule , let u=1+x such that y=u 2 and d...
SG
Answered by Sam G. • Maths tutor
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What is the product rule and when do you use it?

The product rule is used when finding the derivative of the product of two functions - two functions multipled together. If y = f(x)g(x), then dy/dx = f'(x)g(x) + f(x)g'(x) Where f'(x) is the derivative of f...
TJ
Answered by Tom J. • Maths tutor
5403 Views

How do you integrate the function cos^2(x)

At first, you might think that it is possible to perform this integral simply by inspection, using the 'backwards chain rule'. This method would consist of adding one to the power, to get cos 3 (x), then div...
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Answered by Edward R. • Maths tutor
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