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Further Mathematics
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How would I solve the following equation d^2x/dt^2 + 5dx/dt + 6x = 0

Our given equation is d2x/dt2 + 5dx/dt + 6x = 0, which we need to recognise as a second order differential equation. Therefore we need to begin by solving the auxilary funtion m...

DM
5898 Views

Why is the integral of 1/sqrt(1-x^2)dx = sin^{-1}(x)?

This is an example of an integral that uses trigonometric substitutions, which is quite a common theme for A-level further maths questions. Firstly, notice the denominator is quite unpleasant, so to make ...

CB
33169 Views

Take quadratic equation x^2-6x+14=0 and its solutions a and b. What is a/b+b/a?

In this kind of exersise it is easy to use Viète's formula for quadratic equations: Let: a+b = S ab=P then x2 -Sx + P=0 In our case, S=6 and P=14 by multiplying the fractions we get: (a

AM
2511 Views

a) Given f(x) = ln(x), use the Mean Value Theorem to show that for 0 <a <b, (b-a)/b < ln(b/a) < (b-a)/a. b)Hence show that ln(1.2) lies between 1/m and 1/n, with m, n consecutive integers to be determined.

a) f(x)=ln(x), so f'(x)=1/x. By MVT, f'(c) = (f(b)-f(a))/(b-a) = (ln b - ln a)/(b-a) = ln(b/a)/(b-a), where c lies between a and b.  Now, since 1/x is a decreasing function, and a < c < b, we get 1/...

CR
8332 Views

In statistics, what is the benefit of taking a sample survey rather than a census?

Taking a sample survey is quicker, cheaper and easier to carry out than a census. 

EG
3563 Views

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