Math Is Fun Forum

Some corrections.

More precisely, they are not differentiable only at integer values of x. (If x is not an integer they are perfectly differentiable at x.)

Similarly the function so y=x[sup](1/3)[/sup] is only not differentiable at the origin; elsewhere it is differentiable.

The y=1/x and  y=sin(1/x) are not defined at the origin so it makes no sense to ask whether they are differentiable there. To be differentiable at a certain point, the function must first of all be defined there!

And the last part:

Most sincere apologies. I did not read the OP carefully.

The tangent through this point is perpendicular to the line joining their circles, which has gradient

The equations of the circles are

Now subtract [3] from [2] and use the relation [1], and you should get the answer.

I think it’s the most beautiful poem ON EARTH.

Unluckily, natural philosophy was. (I think it was the former name for physics.)

In the novel by Mary Shelley, Victor Frankenstein was a student of natural philosophy at the German university of Ingolstadt when he created his nameless creature.

How could metaphysics be considered a science? Science consists of hypotheses and the testing of hypotheses by experiments, whereas metaphysics is nothing but fanciful, often untestable assertions about stuff. Anybody who considers metaphysics a science must really know sweet FA about science itself.

Not a clue, unfortunately.

The Wikipedia article is very badly written. Also, Wolfram MathWorld has a different definition of matrix polynomial (http://mathworld.wolfram.com/MatrixPolynomial.html) defining it as a polynomial with matrix coefficients rather than matrix variables – but I think the Wikipedia definition makes more sense. In other words, if p(x) is a polynomial, p(A) is the matrix polynomial obtained by replacing the variable x by the matrix A and the constant term by a[sub]0[/sub]I[sub]2[/sub] where I[sub]2[/sub] (= A[sup]0[/sup]) is the 2×2 identity matrix.

I’ve Google-searched but found very little in the way of help on tackling problems of this sort.

I got 35 instead but I don’t know where I went wrong.

EDIT: I got it now. I carelessly used sin instead of tan.

Indeed I hope man becomes extinct. Hopefully, after a few thousand million years, when he evolves back into existence, he will have learnt his lesson and will choose his lifestyle more carefully.

That’s because modern people have been heavily conditioned into worshipping these commodities (computers, cellphones, etc) as life-or-death necessities. All of us are born into a materialistic culture in which money plays a vital part – and with rear the ugly heads of greed, selfishness, egocentric ambitiousness, etc. Suppose we go back to the time of our ancestors before this materialistic culture of ours was developed. Suppose, instead of going down this materialistic pathway, we choose the non-materialistic lifestyle of animals. Then we would live like animals – and money and computers would never have been invented, simply because we would have no use for them in our simplistic, non-materialistic way of life. And because they hadn’t been invented, we would not crave them. You cannot have a craving for things that don’t exist!

—King Lear, Act 1 scene 1