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Consider the curve y=x/(x+4)^0.5. (i) Show that the derivative of the curve is given by dy/dx= (x+8)/2(x+4)^3/2 and (ii) hence find the coordinates of the intersection between the left vertical asymptote and the line tangent to the curve at the origin.

The unsimplified form of the derivative can be obtained fairly easily with use of the quotient rule. The trick for simplification is to multiply top and bottom by (x+4)^0.5, this allows manipulation of th...

Answered by Seb R. • Maths tutor

2985 Views

Integrate 3x^4-4x^2+3/x

Firstly, integrate each term individually, starting off with the 3x^4. In order to integrate the index on the x term needs to be raised by 1, and the coefficient of the x should be divided by this new val...

Answered by Muhammad R. • Maths tutor

3163 Views

How do I get the eigenvalues, x, of a matrix, M, with eigenvectors, v?

To start off, let's write the equation involving these three objects: Mv = xv. Now, looking at the first form of the equation, we don't want any eigenvector to have all its entries be zero, or else the ei...

Answered by Matthew M. • Maths tutor

3705 Views

Solve these simultaneous equations.....3a+2b = 17 and 8a-2b= 60

3a+2b = 178a-2b = 60We are going to solve this using the elimination method. This means that we are going to eliminate the variable (or letter) that has the same value in each equation. In this case it is...

Answered by Joel O. • Maths tutor

4867 Views

Solve the equation x^2 + 10x + 24 = 0

x² + 10x + 24 = 0
First we must factorise the equation, which means put it into brackets. To do this we must find two numbers which multiply to equal 24 and add together to make 10. The on...

Answered by Archie A. • Maths tutor

10223 Views