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Integrate ln(x/7) with respect to x

Firstly split up the ln(x/7) = ln(x) - ln(7) using rules of logarithms learnt in your first year of A-levels, as this will reduce any likely error.Secondly, recognise that the -ln(7) term is constant, and so...
AS
Answered by Arjun S. • Maths tutor
3765 Views

A curve passes through the point (4, 8) and satisfies the differential equation dy/dx = 1/ (2x + rootx) , Use a step-by-step method with a step length of 0.3 to estimate the value of y at x = 4.6 . Give your answer to four decimal places.

h dy/dx (4) = 0.03y(4.3) = 8+0.03 = 8.03y(4.6) = y(4.3) + 0.3 dy/dx(4.3) = 8.0581 to 4 d.p
KW
Answered by Keni W. • Maths tutor
4014 Views

Express 2(x-1)/(x^2-2x-3) - 1/(x-3) as a fraction in its simplest form.

The answer is 1/(x+1)I began by factorising the denominator of the first fraction:2(x-1)/(x^2-2x-3) - 1/(x-3) = 2(x-1)/(x-3)(x+1) - 1/(x-3) Next, I multiplied both the numerator and the denominator of the se...
DR
Answered by Devan R. • Maths tutor
9779 Views

What is the equation of the tangent to the curve y=x^3+3x^2+2 when x=2

dy/dx=3x^2+6xx=2m=3(2)^2+6(2)=24at x=2 y=22(2,22)y-22=24(x-2)y-22=24x-48y=24x-26
KH
Answered by Kieran H. • Maths tutor
4373 Views

Solve ∫(x+2)/(2x^2+1)^3 dx

Since (x+2)/(2x 2 +1) 3 can't be easily simplified into a more straightforward integral, we have to rely on some more advanced integration methods. Before trying things like substitution, or integration by p...
JM
Answered by Jack M. • Maths tutor
6514 Views