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The point on the graph of y = arctan(x) that was at (0,0) gets sent to (3,2) by the transformations, yes.

"Thinner"

Here are the required steps (in order): 1) Take the arctan graph and shift it right 3 units. 2) Compress this vertically by a factor of 2. 3) Shift this up 2 units.

$\noindent If you know the rules for transformations of graphs and what the graph of $y = \tan ^{-1}x$ looks like, then this question should be relatively easy, because those are all you need for this.$

$\noindent Do you know the graph of $y= \tan ^{-1} x$ and about transformations of graphs (like how replacing $x$ with $x-a$ etc. affects the graph of a function $y = f(x)$)?$

Re: Discrete Maths Sem 2 2016 Even without a calculator, we could test n = 1 for that sum decently easily, because then we don't need to sum up terms for the LHS, making it the easiest case to test, (just calculating the RHS would need some work, but it's still pretty easy). In general also...

Re: Discrete Maths Sem 2 2016 I think you just made a typo in the second last line (left out a 3 as a coefficient for the first sum, but I'm sure you had it in your working out on paper), but otherwise looks good. You can (and should!) test formulas like this with easy values of n, e.g. n =...

1) Yes, exclude x = 0, because if x is 0, |xy| = 0, which isn't greater than or equal to 1. The region in question must be symmetric about both coordinate axes. This is because if a point (x,y) satisfies the inequality, so does (+/- x, +/- y), for any independent choices of the +/-. So the...

$\noindent 1. Note that $|f(x)| > |g(x)|$ if and only if $\left( f(x)\right)^2 > \left( g(x)\right)^2$, so you may want to solve this instead. Alternatively, you could consider the absolute value inequality in cases by restricting $x$ in ways that allow you to remove the absolute value signs.$...

The internal marks do matter too (like the relative gaps between people). So being like 1% behind first in internal marks is in general better than being say 10% being first.

Re: Discrete Maths Sem 2 2016 $\noindent For a set $A$, the identity map/function on $A$ (which we can denote $\mathrm{id}_A$) is the function that has domain and codomain $A$ and just maps each element of $A$ to itself. In other words, $\mathrm{id}_A \left(x\right) = x$ for all $x \in A$.$...

Re: Discrete Maths Sem 2 2016 For your last Q., yes, that's true.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread From the 'tangent-secant' theorem, we have 10(10+x) = 12^2 = 144, so 10x + 100 = 144, which implies 10x = 44, i.e. x = 4.4, which is option (B).

Re: HSC 2016 2U Marathon NEW QUESTION $\noindent Let $n$ be a positive integer. Find the $n^{\text{th}}$ derivative of $x^n$.$

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Well quite a few at any rate, e.g. discriminant, complete square, ratio of difference of cubes to difference, single variable calculus, multivariable calculus, use of positive definite matrix etc.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Yeah there's many ways of showing it.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Pretty much all of them.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Hints $\noindent Generally useful: Show that for all real $x,y$, we have $x^2 + y^2 \geq 2xy \qquad (*)$.$ $\noindent 23. Observe that if we treat the given polynomial as a quadratic in $x$ for any given $y$, the...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Use the fact that squares of real numbers are non-negative. What progress have you made so far?

It's a solution because it satisfies that equation (called a differential equation). And the reason they ask you to show that's a solution is also to basically tell you what the solution is (since it is usually needed for later parts); they can't ask "solve the differential equation", because...