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See Also [[Further Maths - Limits]]S Flashcards 2021-11-25 What is L’Hôpital’s rule used for?? Finding the limit of two functions divided together. What is $$\lim_{x \to a} \frac{f(x)}{g(x)}$$ equivalent to?? $$ \lim_{x \to a} \frac{f'(x)}{g'(x)} $$ What technique could you use for finding the value of $$\frac{\sin(x)}{x}$$ at $x = 0$?? L’Hôpital’s rule. What are the conditions for applying L’Hôpital’s rule for $$\lim_{x \to a} \frac{f(x)}{g(x)}$$?? $$ \frac{f(x)}{g(x)} = \frac{0}{0} $$

See also: [[My Experience with the Online Imperial Admissions Process]]B . I’m writing this post because before my interview I had a lot of questions about what it was going to be like, but couldn’t really find much information from people who had already had one. For some context, I made my UCAS application on October 11th 2021 to the following universities: Oxford, Mathematics and Computer Science Imperial, Mathematics and Computer Science UCL, Mathematics and Computer Science Southampton, Computer Science with Artificial Intelligence Bristol, Mathematics and Computer Science And received a Imperial offer for A*A*AA with Grade 2 STEP requirements.

Flashcards 2021-11-24 What is the derivative of $$y = uv$$?? $$ u \frac{\text{d}v}{\text{d}x} + v \frac{\text{d}u}{\text{d}x} $$ What is the derivative of $$\frac{\text{d}y}{\text{d}x} = u \frac{\text{d}v}{\text{d}x} + v \frac{\text{d}u}{\text{d}x}$$?? $$ u\frac{\text{d}^2v}{\text{d}x^2} + \frac{\text{d}u}{\text{d}x}\frac{\text{d}v}{\text{d}x} + v\frac{\text{d}^2u}{\text{d}x^2} + \frac{\text{d}u}{\text{d}x}\frac{\text{d}v}{\text{d}x} $$ What does Leibnitz’s theorem give a general formula for?? The $n$th derivative of the product of two functions. What is $\frac{\text{d}^0v}{\text{d}x^0}$?? $$ v $$ What is the formula from Leibnitz’s theorem for the $n$th derivative of $y = uv$?

Flashcards 2021-11-20 What is the formula for the maximum friction?? $$ F_\text{max} = \mu R $$ What is $\mu$ when talking about friction?? The coefficient of friction. What is $\mu$ if a surface is described as “smooth”?? $$ 0 $$ If a block is being pushed with a $10\text{N}$ force but there is a $20\text{N}$ max friction, what will happen?? The block will not move. What is the situation called when a block is being pushed with a $20\text{N}$ force but there is a $20\text{N}$ max friction?

Flashcards 2021-11-20 What is the angle beneath the red block?? $$ 3\text{kg} $$ What is the resultant force in this diagram, assuming no resistive forces?? $$ 3g\sin(30^\circ) $$ What is the resultant force in this diagram?? $$ 2g\sin(20^\circ) - 2 $$ What is the resultant force in this diagram?? $$ 5g\cos(60^\circ) - mg\sin(30^\circ) $$ 2022-01-20 What will happen to the direction of friction for an object moving up a slope but accelerating downwards?? It will flip direction when the object flips direction.

See Also [[Physics - Kepler's Laws]]S Flashcards What is the equation for gravitational field strength, $g$?? $$ g = \frac{F}{m} $$ What are the two possible units for gravitational field strength?? $$ \text{N}\text{kg}^{-1} $$ $$ \text{m}\text{s}^{-1} $$ What is the wordy explanation of gravitational field strength?? The gravitational force exerted per unit mass on a small object placed at a point within the field. What simplifying assumption do we make for planets and stars when calculating gravitational fields?

Flashcards How could you summarise the route inspection problem?? Find a route of minimum weight that traverses every edge at least once, starting and ending at the same vertex. Why will a Eulerian trail solve the route inspection problem minimally?? Because it traverses every edge exactly once, so it keeps edge weights to a minimum. When there are two odd verticies and you’re trying to solve a route inspection problem, what should you do?? Find the shortest route between them and double those edges.

Flashcards What are the three values you should store for each vertex in Dijkstra’s?? Once you’ve labelled the end vertex with a permanent label in Dijkstra’s, what can you do?? Stop and save yourself the work of labelling every vertex. What does Dijkstra’s algorithm do?? Tell you the shortest distance from any node to the start node. At each step of Dijkstra’s algorithm, what should you do?? Look at the verticies connected to the most recently permanently labelled node.

Man’s experience rises from a physical basis, but man has no good explanation of why and how it arises. Why should man get rich inner life? I read this but didn’t highlight any of it, so most of my notes come from Book Review: Being You by Anil Seth on LessWrong. Notes Measuring consciousness We now have technology that lets us point sensors at people’s heads and tell whether they are conscious even if they have full locked-in syndrome.

Flashcards What are the 5 assumptions made for an ideal gas (VVETE)?? There are lots and lots of particles with random velocities. The individual particles have much smaller volumes than the volume of the gas. The collisions with container walls are perfectly elastic. The duration of collisions is much smaller than the duration of not-collisions. The electrostatic forces are negligible expect for during collisions. Why is the assumption that collisions between particles and container walls being perfectly elastic useful?

Flashcards What is the $y = x$ equivalent for polar coordinates?? $$ r = \theta $$ What is $x$ in terms of $r$ and $\theta$ for polar coordinates?? $$ x = r\cos\theta $$ What is $y$ in terms of $r$ and $\theta$ for polar coordinates?? $$ y = r\sin\theta $$ What is $r$ in terms of $x$ and $y$ for polar coordinates?? $$ r = \sqrt{x^2 + y^2} $$ What is $\theta$ in terms of $x$ and $y$?

See Also [[Further Maths - Radians]]S Flashcards What is the small angle approximation for $\sin \theta$ and $\tan \theta$?? $$ \sin \theta \approx \tan \theta \approx \theta $$ What is the small angle approximation for $\cos \theta$?? $$ 1 - \frac{\theta^2}{2} $$ What is $$\frac{\tan 2\theta}{\sin \theta}$$ for $\theta \approx 0$?? $$ 2 $$ Backlinks [[Maths - Syllabus]]S Metadata date: 2021-11-09 15:30 tags: - '@?public' - '@?