Search our library of Maths A Level questions

Top answers

Maths

A Level

Integrate ln(x) by parts then differentiate to prove the result is correct

Integrating by parts requirez recognition that ln(x) is equal to ln(x) multiplied by 1. Making u equal to ln(x) should make the integration trivial. Differentiation is a simple use of the product rule and...

Answered by Joshua D. • Maths tutor

4475 Views

The line AB has equation 3x + 5y = 7. Find the gradient of line AB.

First, let's make y the subject of the equation.

Let's achieve this by having only y on the left hand side of the equation. To do this we need to minus 3x from both sides of the equation. This leav...

Answered by Tom O. • Maths tutor

5358 Views

The volume of liquid in a container is given by v=(3h^2+4)^(3/2)-8, find dV/dh when h = 0.6

Chain rule: dV/dh=9h(3h^2+4)^(1/2)
sub in h=0.6 , dV/dh = 12.17

Answered by Johnny H. • Maths tutor

8732 Views

Given that y=(4x^2)lnx, find f"(x) when x=e^2

Product rule: first order derivative = 8xlnx+4x Second order derivative = 8lnx+12 Sub in e^2 , 16lne + 12 = 24

Answered by Johnny H. • Maths tutor

5001 Views

What is the difference between differentiation and integration, and why do we need Calculus at all?

We need calculus to find out the properties complex curves that we cannot find with simple arithmetic as we would with linear graphs. Differentiation allows us to calculate the gradient of a curve at a sp...

Answered by Samuel H. • Maths tutor

9726 Views