Recent content by JamesGoh

Homework Statement See the document attached as it contains a diagram Homework Equations cos(theta) = adjacent/hypotenuse, sin(theta) = opposite/hypotenuse, tan(theta) = opposite/adjacent The Attempt at a Solution See document attached

Stephen, yes integration along AD is what I am asking about. SteamKing, I did notice that there was no change in y coordinate. However, why would the curve integral be 0 (as the answers say)? It makes no sense as some force is used to move the particle from A to D so it cannot be 0?

Im doing some revision of vector calculus and came across the following problem Q: Calculate the work done by the force field F = 3xyi - 2j in moving from A: (1,0,0) to D: (2,0,0) and then from D: (2,0,0) to B: (2,sqrt(3),0) I got stuck and decided to look at the answers. In the answers (part...

Im trying to find the integral of ( sec(t)^2 ) / ( (tan(t)^3) + (tan(t)^2) ). I've managed to get the integral into the form 1 / (u^3 + u^2) where u = tan(t), however I am having difficulty proceeeding from there. Could someone take a look at the working out I have attached and let me...

For this function y=\sqrt{2ln(x)+1} if I use the chain rule properly, should I be getting this answer? \frac{dy}{dx}=\frac{2}{x} \times \frac{1}{2} \times \frac{1}{\sqrt{2ln(x)+1}} My aim of doing this is to verify that \frac{dy}{dx}=\frac{1}{xy}

sorry wrong piece of paper. Please look at this new attachment and inform me of my error

To the original poster, I would say invest some time looking into the job market and any astrophysics or science societies before deciding to change degrees. I was interested in wireless communications during my undergrad degree, but job prospects were quite low, so I am now studying to...

For the following problem \frac{dw}{d\theta}=\theta w^{2}sin(\theta^{2}), w(0)=1 I am not able to obtain the solution w=\frac{2}{1+cos(\theta^{2})} Can anyone point out my mistake? I have attached my working out in a picture format below (may need to enlarge it) thanks

Is the following statement valid? sinh{x^2}=\frac{e^{x^2}-e^{x^2}}{2} Reason I ask cause I know that sinh{x}=\frac{e^{x}-e^{x}}{2}, so i assume the same rules can apply

What is the indefinite integral of cosec(\theta)?

For a normal distribution with E[x]=0 and Var(X)=1, how do we determine the Z-value of a particular percentage ? i.e. if the percentage is 5%, how do we know that Z(5%)= 1.645 ? is there a calculation involved or do we get it from observing the x-axis of the normal distribution ?

To differentiate cos(yz^{2}) with respect to y can we simply ignore the z^{2} term in the differentiation ?

Does this case of "standard basis" only apply for any 3-element vector input written in the form of a parabolic equation ?

What button in the text formatting allows you to create perfectly aligned matrices ?

Homework Statement Given the following defined transformation T(a + bt+ct^{2}) = (a+c) - (c+b)t + (a+b+c)t^{2} find the matrix with respect to the standard basis From my understanding, the standard basis for a 3 element vector would be (0,0,1)^{T} (0,1,0)^{T}...