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Starts it off differently with: http://imgur.com/xkKGwfx (it continues based off this) I don't really like this approach because of the manipulation from step 4 to 5

Show that sin^3x(cos^2x) = 1/16 (2sinx +sin3x -sin5x) (using the fact that z + 1/z = 2cosx, and z - 1/z = 2isinx) My approach was to expand LHS into sin^3x (1-sin^2x) = sin^3x - sin^5x = (z - 1/z)^3 - (z - 1/z)^5 (then expand and simplify) Is this a viable method? The suggested...

Y = x^2 + 2x, bounded by x = -1 and x = 2. Using a single intergral results in an incorrect answer. Looks like for every positive parabola with a negative boundary, two integral are required. Any other cases for this?

In what cases is it required to split an integral into seperate components in order to get the appropriate answer. Some questions I find require you to split a single integral into two or more parts. Is there a general case in which this applies?

http://m.imgur.com/SeuqmHu Idk what to do for the first one For the second, I used sum of gp, but couldn't get the answer. Answers are 16root2(cos^4(pi/16)) and (1+root2)i respectively *edit - for the second q, mistakenly took n to be 20 instead of 21.

woah, so OP. Thanks!

For the argument component, it is stated that theta = 2kpi / n For example, if z^3 = 1, the arguments are 0, 2pi/3 and 4pi/3 What happens to negative numbers, such as z^3 = -1? Is it the same thing, but for odd numbers such as pi/3 , pi, 5pi/3? Thanks.

um.. do what carrot wrote. Basically, let alpha = -2, and beta, gamma = A Find sum and product of roots and solve simultaneously

Whoops, I made a slight error. When i said that your max sp would be the max value within your domain, i was incorrect. In this case, by testing values at the domain, x = 3 has the highest value, because f(3) = 13

And your max pt will be your max value within the domain

for a), it is inferred that you find the stat pts. By differentiation, x = +- (root) 2 and y = (approx) -1.66 and 9.66 respectively From here, you can already tell which ones are max and min, but to be sure, you can use the table method to determine the roots. *Note that since it asks to...

http://imgur.com/iVqgqAj Generally, all 'turning point' questions follow the same process: 1. Differentiate 2. Let the derivative = 0 3. Solve for x 4. Sub x back into f(x) to find the coordinates - If they ask for you to determine the nature, you can use either the table method or the second...

In what ways has the World Bank contributed to Globalisation?

Find other angles by separating to individual triangles

Cool question

I bet 100 on: faisal mreditor triage

does this law basically state that the derivative of the anti-derivative = function? Could this fact be useful for HSC math? and for what circumstances? thanks.

Hello, I need some guidance with this q http://imgur.com/TtisiTV The algebra is putting me off.

Alliteration, personofication

When y''= 0, you're essentially finding any points of inflexion. I'm not sure where you got the 'vertical' from. Horizontal points of inflexion occur when there is also a stat. pt. at that particular point. That is because the tangent at that point is horizontal.