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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I thought the nth derivative of x^n was n! or n(n-1)(n-2) ... 1

I believe it oscillates around the point it is pictured at in the diagram. But I also believe if it were to be in that point initially, it wont oscillate.

http://i.imgur.com/LUm5sLU.png I answered A but the answers say D. The motor will rotate continuously with an AC source, that I know. In the picture though, the motor is in a position which I believe won't experience any rotation if connected to a DC source, which is why I chose A. Am I...

Thank you both very much. I hate that I have been taught up until now that the derivative is just an operator or symbol. Only now must I use it as a quotient of infinitesimals as KingofActing said. On that note, why do you get t when you integrate dt?

Could someone show me how to do this? $If $\frac{dx}{dt}=\frac{1}{x+4}$ and $x=0$ when $t=0$, find t when $x=2

Re: HSC 2016 2U Marathon \\2^x+2^{x+1}+2^{x+2}+\cdots +2^{x+2015}=4^x+4^{x+1}+4^{x+2}+\cdots +4^{x+2015}\\2^x(1+2+2^2+2^3+\cdots +2^{2015})=2^{2x}(1+4+4^2+4^3+\cdots 4^{2016})\\1+2+2^2+2^3+\cdots +2^{2015}=2^x(1+4+4^2+4^3+\cdots...

As leehuan pointed out, the induced emf is proportional the the rate of change of flux. At the instant the plane of the coil is parallel to the magnetic field, the flux threading the coils is changing at a high rate. This is because the "catchment area" of the loop for magnetic flux lines...

Thank you, but I'm going to need a little bit more than that. I take it I need to eliminate p, how can I do that?

The question must be meaning a serial number which has 4 letters, followed by 2 numbers, in that order. There would be more combinations than 37015056 if the serial numbers allowed letters and numbers to be in any order. This is what I don't like about permutations and combinations, the...

If someone could do a worked solution for part ii that would be great. I have already done part i. $The line through O the origin is perpendicular tot he tangent at $P(cp,\frac{c}{p})$ on the rectangular hyperbola $xy=c^2$ meets the tangent at N. You may assume this tangent has the equation...

Questions are never repeated, but can come in the same form. After doing a lot of past papers, you begin to realise the patterns of questions and can complete questions faster as you recognise the best methods to do them while others are still exploring them.

Cheers.

In a test, would we be allowed to assume the identity \frac{x_0x}{a^2}-\frac{y_0y}{b^2}=1 for chords of contact, or would we have to prove this? If a proof is required, how would we prove it?

Can someone show how you would set out working for this question? \\$Find the equation of the chord of contact of the tangents to $x^2-16y^2=16$ from the point $(2,-3)$.$

I've added the second one into my post now.

I think this question is actually within the 3U syllabus. First graph: http://i.imgur.com/bsxs98p.jpg Second graph: http://i.imgur.com/LXFATpP.jpg

You are thinking about the function's domain and what x values it cant have. We need to be thinking about what y values it will never be. \frac{1}{\sqrt{2x+9}} The denominator is a principal root, which is always positive. One on something that is always positive is going to be always...

Trapezoidal rule is pretty straight forward: an application has one subinterval and for n applications there are n+1 function values. The Simpson's rule is a little more complex: one application has two subintervals. This means there is a beginning, middle and end function value for each...

Thanks

Right, I get how you found the root of the derivative, or the square of the root for that matter. Did you get the quoted line from subbing that back into the original equation? If so, shouldn't there be 3 terms seeing as x^5-tx^2+q=0 is the original equation?