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In continuation to my previous post, for this question: I got the first two parts. However, when I did (c), this is what I get: This has got all the terms that have been asked in (c), so I know I've expanded correctly, but, for some reason, there are two extra terms in the answer to (c)...

Thanks Any thoughts on this btw?

Also, forgot to add, to find time for when the cat is descending, just used the delta y equation I've provided above with delta y = -2 and u = 0. Hope this helps :)

Got it \\\text{We also know }\\\int_{x_0}^{x_1}|u(x)|dx\leq\left|\int_{x_0}^{x_1}u(x)dx\right|\\\therefore\text{The above stated inequality is true} For this question, I use the fact that as the curve of u(x) is always less than or equal to the curve of the RHS inequality, the area under the...

\text{1(a) v =} \int (1-sin^2t)dt = \int cos^2tdt = \frac{1}{2} \int (cos2t+1)dt\\=\frac{1}{2}\left(\frac{1}{2}sin2t + t\right)+C\\\text{Now when t = 0, v = 0, so C = 0, so }v=\frac{1}{2}\left(\frac{1}{2}sin2t + t\right) 1(b) When t = 0, the particle experiences acceleration = 1-sin^2(0) = 1...

Thanks, and what about the RHS of the inequality, K/24 h^3?

Thanks. But I don't get the logic behind this... And why does the integral of f'(m1)(x-m1) =0?

To start with, use a digital scale, not a non-digital one. I guess one of the most important suggestions to this experiment would be to use a VERY strong magnet and a solenoid with lots and lots of coils because on such a small scale, the current passing through the wire may not be enough for...

True. I meant that you should do papers under timed conditions. But as Rathin stated, he knewhow to do most of the questions, so I don't think content is the problem...

When the cat is jumping up, there is a vertical displacement of 4m. Assuming the cat is on Earth and has unit mass, the cat experiences a downward pull from gravity of -9.8ms-2. Note that when the cat is 4m into the air, its velocity would be zero and then it would return back to the ground. The...

While skipping harder questions and redoing questions is great advice, I personally found that the best way to have perfect timing in maths tests is to do as many papers as you can. This is because everyone's exam technique is different when it comes to maximising marks under timed conditions...

Thanks. There is another question similar to the MVT one above. I'll try to do attempt that one as well as I didn't get it before. How would you do this one? \\\text{(The Error Estimate for the Midpoint Rule) If }x_1-x_0=h \text{ and }m_1\text{ is the midpoint of }[x_0,x_1]\text{ use the...

Thanks \\\text{Suppose }f\text{ has a continuous 2nd order derivative }f''.\text{ Use integration by parts to show that }\\\int_{0}^{1}f(x) dx-\frac{1}{2}(f(0)+f(1)) = -\int_{0}^{1}f''(x)\frac{1}{2}x(1-x)dx\\\\\text{Use the Mean Value theorem for integrals to deduce that there is a real number...

Thanks everyone for your replies! I have this other question. For the first part, I get V'(x) = u(x)(a-x). If this is right, how would you do the second part?

Lol I think both of you guys are right.

And when making the substitution, how would you account for the upper limit, do we just say: As u = lnx, u-->infinity as x-->infinity so the upper limit of the integral after the substitution would be infinity

Oh right, so when p>1, this integral would converge according to the p-test... But how would you account for the limits, isn't it a condition of the p-test to have the lower limit to be 1 and upper limit to be infinity. I guess I could just say it doesn't matter if you start taking area from...

Sorry, I don't understand it. That's alright, I'll just ask my tutor. Thanks anyway :) Meanwhile, I've another question: \\\text{Find all real numbers }p\text{ such that } I = \int_{2}^{\infty} \frac{1}{x(lnx)^p} dx\text{ converges}

How would you rearrange this to get [2^(j+1)-1]/n ? I'm stumped lol

I'm somehow struggling with Riemann sums and Riemann Integrals, so if you could provide a general approach when solving such questions by solving this one, that would be great...I understand the concept and I get the formula, just need a rigorous approach for such questions...