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Sketch the curve y = (2x-1)/(x+1) stating the equations of any asymptotes and coordinates of the intersection with the axis. As an extension, what standard transformations from C1 could you use on y=1/x to get this curve?

A good way to start with any of these questions is to guess what type of curve this is, and if that is too difficult then the next best thing is to find some points. In this case it is obvious that it is ...

Answered by Alex D. • Maths tutor

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Differentiate x^3 + 6x + 1

Though you are required to understand differentiating from first principles for the exam, questions such as this become quite straightforward once you know the trick.
To differentiate all you have to...

Answered by Myles J. • Maths tutor

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differentiate with respect to x. i). x^(1/2) ln (3x),

From this we can see that equation has 2 parts therefore we should look to using the product rule which is used to differiantiate a two functions multiplied together so (fg)'=f'g+fg'. In this question the...

Answered by Jesse D. • Maths tutor

6583 Views

Prove the change of base formula for logarithms. That is, prove that log_a (x) = log_b (x) / log_b (a).

Firstly, recall the definition of a logarithm: if y = log_a(x), then this means that y is the power you have to raise a to, to get x, that is a^y = x.Now, we want to introduce a new ba...

Answered by Tom H. • Maths tutor

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(ii) Prove by induction that, for all positive integers n, f(n) = 3^(3n–2) + 2^(3n+1) is divisible by 19

Let P(n) represent the statement that 'f(n) is divisible by 19'. For the basis step, I prove that P(1) is true: f(1) = 3^3(1)-2+ 2³⁽¹⁾⁺¹ = 19. 19 is divisible by 19 so P(1) is true. I...

Answered by Daniel L. • Maths tutor

9446 Views