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Hi sasquatch, (16 - x2)/x2 = 16/x2 - 1 Therefore: ∫(16 - x2)/x2 dx = ∫16/x2 dx - ∫1 dx = -16/x - x + C Hope that helps. P.S. Riviet how can you just jump to the conclusion that he's looking for a more advanced technique? Maybe there are people out there who are genuinely...

Thank you shsshs. Unfortunately, nice but not great.

EDIT:

Hi shsshs, Question 1a): i) Both parts a) and b) involve statements about the velocity(remember vectors: directions as well) of the projectile at point of contact. A natural question would then be "what is mathematically related to the direction/angle of velocity"? A: The gradient of the...

Hey sando, Question 1: The equation of interest is ln(x) = y ---> x = ey , because you will be integrating with respect to dy: I = {4 -> 2}∫ey dy = [ey]{4 -> 2} = e4 - e2 = e2(e2 - 1) units2 Question 2: Once again, the equation of interest is x = ey for the same above reason...

? Umm... unfortunately no McSo, since the condition that the tangent be perpendicular to PQ is exactly what you are trying to find in the first place! But of course once you have shown that, then a simple geometric argument following that will suffice towards the final proof. (i.e. that...

You don't say! :rolleyes: haha.

This is why "rough" sketches are dangerous in maths... The reason you think the normal is perpendicular to PQ is most probably because you are drawing the three points P, Q, R on the same branch of the hyperbola Riviet. This cannot happen, as you will see with a more accurate diagram. The...

Looks like the normal is fine from here Riviet.

Don't stress out about G.P.'s ppl, after all, the greatest French mathematician (and generally the greatest intuitionist) of all time Henri Poincare did not even know how to prove the formula for the sum of a G.P. during a matriculation exam! (of course, he was under pressure from being late...

Hey, Divide the 'x' throughout each term of the numerator: ie. (2x³ - x² + 5x + 3)/x = 2x³/x - x²/x + 5x/x + 3/x = 2x2 - x + 5 + 3/x And so: I = {2 -> 1}∫(2x³ - x² + 5x + 3)/x dx = ∫2x2 dx - ∫x dx + ∫5 dx + ∫3/x dx = (2/3)[x3]{2 ->1} - (1/2)[x2]{2 ->1} + 5[x]{2 ->1} + 3[ln(x)]{2...

The Principle of Mathematical Induction (both the weak and strong version, coupled with other techniques oftened called "backward induction") is a principle in mathematics used often to prove mathematical statements that generalise into an infinite class/family of numbers. It is a principle that...

Part a) {apologies for my poor illustration skills...} Part b) Differentiate the expression with respect to t to obtain velocity v = dx/dt: v = dx/dt = 4Sin(2t) Rest means v = 0: 0 = 4Sin(2t) = Sin(2t) -----> t = (1/2)k.pi ; where k is a nonnegative integer and "pi" is your...

Thanks for correctin' the record Kidmin ;)

As Kid.@dmin has said him/herself which you quoted: "...shall results in a very... stupid me." It wasn't necessary that you paid reminder to the stupidity part again... wasn't very nice now was it? Anyways, back to the original discussion on calculators... isn't it a shame that it's become...

though admittedly, one wouldn't consciously choose ANU for that particular field of study as an undergraduate unless one did not have a choice... (if you are interested in immunology, pathology, and/or microbiology, take a look at UM or UQ as well.)

'tis indeed false. usually, honours are offered in every discipline for which a major may be obtained in the (usually) three years prior to the 4th.

^ Yes, that's the Frank I was talking about - we're in the same class (you're in it too aren't you?). Btw, best of luck with your 2301 exam on Thursday Steele :) . (and all your other exams also)

^ ? no unfortunately, though I do know Frank (from the same school as Vinh right?) :) .

Hi ... , hope this is still in time to be of some help to you. From what I can see, there are three ways of (formally) solving this problem: 1) Calculus, 2) Geometry, or 3) Inequalities; all of them beyond HS level mathematics. Since in mathematics any geometrical solution is usually the...