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find the integral of 1+3 root x

now for any integral the method to deal with it is look for the easiest method, things can get trickier later down the line but always start by looking for the easy solution. this example allows us to see...

HD
Answered by Harry D. Maths tutor
4496 Views

The element of a cone has length L. For what height H (with respect to L) will the volume of the cone be the largest?

This is a good exercise to introduce student to the idea of derivatives and their possible practical use.
Firstly, I should draw the cone and notice that its volume is equal to 1/3piH*R

MK
Answered by Max K. Maths tutor
3691 Views

Consider the arithmetic sequence 5,7,9,11, …. Derive a formula for (i) the nth term and (ii) the sum to n terms. (iii) Hence find the sum of the first 20 terms.

We can easily identify the first term (5)

The common difference can be found by subtracting the nth term from the (n+1)th term

7-5=9-7=11-9=2

Therefore:

U...

JN
Answered by Jan Niklas F. Maths tutor
6610 Views

Differentiate y=(3x-1)/(2x-1)

First, recognise that the function is a fraction and recall the quotient rule.     y=u/v     dy/dx=(vu'-uv')/v2, where u' and v' is the derivative...

MM
Answered by Martin M. Maths tutor
6919 Views

Rationalise the following: { 5 } / { 3 - sqrt(2) }

The aim here is to turn the fraction so that the denominator does not have a surd. 

Given that we know that any surd squared is equal to the number itself, i.e sqrt(2) * sqrt(2) eq...

AS
Answered by Amin S. Maths tutor
5407 Views

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