Tag Archives: proof

Sum of two metrics is a metric

It is quite straightforward to prove or verify that the sum of two metrics (distance functions) is still a metric. Suppose and are metrics. Define . Positive-definite . . Symmetry . Triangle Inequality Note that it follows by induction that … Continue reading

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Second-derivative Test For Extrema Of Functions Of Two Variables

Source: http://www.math.illinois.edu/~verahur/18.024/notesSD.pdf Excerpt:  Proof of the second-derivative test. Our goal is to derive the second-derivative test, which determines the nature of a critical point of a function of two variables, that is, whether a critical point is a local minimum, a local maximum, … Continue reading

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Proving Quotient Rule using Product Rule

Proving Quotient Rule using Product Rule This is how we can prove Quotient Rule using the Product Rule. First, we need the Product Rule for differentiation: Now, we can write Using Product Rule, Simplifying the above will give the Quotient … Continue reading

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Infinite Primes Proof by Euclid

How do we know there are an infinite number of primes? Dr James Grime explains, with a bit of help from Euclid.

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