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Why is it that the sum of all natural numbers up to n is 1/2(n)(n+1)?

First let's consider the case of even numbers. Suppose n is even, then it must be double some other number, so we have: n = 2k Where k is another natural number. We want to find out what: 1 + 2 + ... + (n - ...
IM
Answered by Ibrahim M. • Maths tutor
4758 Views

Find dy/dx in terms of t for the curve defined by the parametric equations: x = (t-1)^3, y = 3t - 8/t^2, where t≠0

The first step is to recognise that, by the chain rule, dy/dx = dy/dt * dt/dx. dy/dt and dt/dx can both be found by differentiating the functions given in the question, to give dy/dt and dx/dt. dt/dx is the ...
AC
Answered by Alex C. • Maths tutor
21960 Views

integrate the following: 2x^4 - 4/sqrt(x) +3 with respect to x

The 3 terms of this equation can be integrated separately. The general integration of x n is (x n+1 )/n+1 where n is a real number not equal to -1. This can be applied to the terms 2x 4 , -4/sqrt(x) and 3 se...
AF
Answered by Adrien F. • Maths tutor
4079 Views

Why is the derivative of the exponential function itself?

The exponential function is defined as a power series, which we may (for reasons that are beyond the scope of A-level) differentiate term by term to get another power series. The general term of the series d...
GB
Answered by George B. • Maths tutor
5099 Views

evaluate the integral of lnx

this is an example of an integration by parts problem, we must use integration by parts to evaluate this integral;although this would not be entirely obvious as the integral does not seem to be the product o...
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Answered by Aaron R. • Maths tutor
3516 Views