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2^2x - 6(2^x ) + 5 = 0let y = 2^xy² - 6y + 5 = 0(y-5)(y-1) = 0 y=5, y=12^x = 5, therefore, x = log₂5 = 2.32 (3 s.f.)2^x = 1, therefo...

Firstly, establish that the correct method to do this is via differentiation: specifically implicit differentiation. To find the gradient, we need to find dy/dx. The differential with res...

As f(x) is in the form of u(x)/v(x) we can apply the rule that f'(x) = (u'(x)*v(x) - v'(x)*u(x))/(v(x)²), pulled from the C3 formula booklet.
If u(x) = sin(2x) then u'(x) = 2cos(2x).
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f(f (x) )= f( (1-x)/(1+x) ) = (1-(1-x)/(1+x))/(1+(1-x)/(1+x))where you replace x by (1-x)/(1+x). Multiply the top and bottom of the fraction by (1+x) to get ((1+x)-(1-x))/((1+x)+(1-x)) which simplifies t...

The normal distribution is a distribution we can use when we know the mean and the standard deviation of a population, to work out probabilities that a certain even will occur.
The main properties of...