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How do I show (2n)! >= 2^n((n!)^2) for every n>=0 by induction?

First we need to be clear how to construct a proof by induction. It has two main parts, the base case and the inductive step. Let P(n) denote that the statement ...

Answered by Connor F. • Maths tutor

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How to find a modulus and argument of w that is a quotient of z1 and z2 such that z1 = 1 + root(3)i and z2 = 1+ i using modulus-argument form?

First of all, transform both z₁and z₂ into modulus-argument form. To obtain that form, you are going to need a modulus (the length of the hypotenuse on the Argand diagram) and argum...

Answered by Piotr S. • Maths tutor

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Given the parametric equations x = lnt+t and y = sint calculate d^2y/dx^2

First we can write d²y/dx² as (d/dx)(dy/dx). Now we need to find dy/dx. This can be further written as (dy/dt)(dt/dx). These derivatives can be obtained from the given parametric equ...

Answered by Agnieszka R. • Maths tutor

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Integrate x^2/(1+x^2)dx

Unlike if we had just x in the numerature, here the chain rule will do us no good. Integration by parts in this case also is little help - we end up with expressions at least as difficult as we started w...

Answered by Laird H. • Maths tutor

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