Top answers

Suppose that 3=2/x(1)=x(1)+(2/x(2))=x(2)+(2/x(3))=x(3)+(2/x(4))+...Guess an expression, in terms of n, for x(n). Then, by induction or otherwise, prove the correctness of your guess.

We have 3=2/x 1 =x 1 +2/x 2 =x 2 +2/x 3 =x 3 +2/x 4 =.... How can we guess at a general expression? One way is to try and see one by looking at the first few terms and looking for a pattern. We can calculate...
GC
Answered by George C. • STEP tutor
1561 Views

Given that the binomial expansion of (1+kx)^n begins 1+8x+16x^2+... a) find k and n b) for what x is this expansion valid?

a) We compare the expansion given to the standard binomial expansion (remembering the powers of k).(1+kx) n =1+n(kx)+(n(n-1)/2)(kx) 2 +...As this is true for all x (for which the expansion holds), we can com...
GC
Answered by George C. • Maths tutor
5901 Views

Given that y=(sin4x)(sec3x), use the product rule to find dy/dx

First, recall the Product rule: f(x)=g(x)*h(x), f'(x)=h(x)*g'(x)+h'(x)*g(x)This reveals the next step, to find the derivatives of our two subsidiary functions(g and h) d/dx * (sin4x) = 4cos(4x) , and d/dx (s...
EF
Answered by Edward F. • Maths tutor
4491 Views

What is the defining characteristic of Cubism?

A multifaceted and enigmatic style of modern art, Cubism is defined primarily by its break with art historical tradition. Launched by Picasso and Braque in the first decade of the twentieth-century in Paris,...
AS
2942 Views

Distinguish between the structure of plant and animal cells

A number of differences exist between the structure of animal cells and plant cells. The most prominent difference is the presence of both cell walls and cell membranes in plants, while animal cells only hav...
JK
Answered by Joanna K. • Biology tutor
3282 Views