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NOTE: There is an error in the first question, I wrote "... in terms of sinh^2(2A)..", it should say "... in terms of sinh^2(A)..". Will fix this soon.

They don't have answers, but I can type up some sample answers/guidelines soon so you can see how you go.

Here you go, let me know if the link doesn't work: https://www.dropbox.com/s/zdku0k0kk26jacg/MATH1151%20CALCULUS%20S1%202014%20-%20TEST1.pdf?dl=0 (You don't need an account, just close the login window and the pdf should open) Hope it helps :)

Sure, one moment.

There really isn't much you can use to prepare for these quizzes, apart from the Calculus Problem Set and past tests. Just do your best to understand everything that will be tested, that will ensure you can get the best marks possible. I can upload my quiz from last year so you may get a feel of...

Re: HSC 2015 4U Marathon - Advanced Level NEW QUESTION: $ Given that $f$ is a continuous function on $\mathbb{R}$ such that $f(0)=0$ and $\lim_{x\to\infty} f(x)=0$, prove that $f$ attains a maximum on $[0, \infty)$. Don't know if this was the right place to post this q.

I guess a more intuitive method would be to consider the fact the each of the 10 basis vectors (in R^10) are all orthogonal (perpendicular) to each other and each lie on its corresponding 'axis', so the only way in which an 11th such vector can be equidistant to these vectors is if it is...

Fair enough

But how would you know all components need to be the same? Why can't they be different?

Fair enough then, I asked because then maybe I could have reasoned out what they meant and tried to deduce some easier way of solving this, especially if it took them around a minute to do (unless they knew the q beforehand, and pulled the quadratic of out nowhere). Wonder if anyone else can...

Do you remember what your tutor said?

Your working seems correct, but I think OP would also want a justification as to why each component of the 11th vector need to be equal, otherwise you wouldn't really be getting the same distance for EVERY pair. To make things simpler, try the exact same case for R^2 and R^3 (where you would...

$ For some 11th vector in $\mathbb{R}^{10}$ if we consider the distance between two vectors, we have $(x_1 - y_1)^2 + (x_2 - y_2)^2 + ... + (x_j - y_j)^2 + ... + (x_{10} - y_{10})^2 = 50$ for ${1\leq{j}\leq10}$. So the question boils down to what are all the possible ways we can write 50 as a...

You forgot to differentiate (1 + x), it should be -d/dx(1+x) NOT, -(1+x) [third last line].

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Sorry for the dodgy LaTex, fixed it up now. The answer is 1/2 since the integral is -1/x, no logarithmic function involved.

$ SOLUTIONS $ \\\ $ (i) $$\int_{1}^{2} \frac{1}{x^2} dx$$=\frac{1}{2}$ \\\ $ (ii) Standard integral of exponential function (use table to refer). $ \\\ Q6. $$\int\frac{x}{x^2+3}dx$$=$$\frac{1}{2}\int\frac{2x}{x^2+3} dx$$=$$\frac{1}{2}\ln{|x^2+3|} + C$$ $ \\\ $ \\\ \\\ Q7. $ If $\log2=x$ and...

Re: HSC 2015 3U Marathon ALTERNATE WAY: $ 1. The number of ways in which ONE meal is NOT chosen is ${6 \choose 1}$ \\ 2. The number of ways in which one meal is selected exactly twice is ${5 \choose 1}$. \\ 3. The total number of ways in which the diners can be assigned to the meals is...

Re: HSC 2015 3U Marathon Ah, I see what you have done, your explanation seemed a bit dodge so I misinterpreted what you said, your answer is correct :)

Re: HSC 2015 3U Marathon You seem to have the right idea, but note that each diner chooses only one meal each, you can't have 4 meals for one diner. I'll post up my solution soon.