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Oh yes, I meant the latter. Sorry for the confusion that it may have lead to.

It is a tough call, since now I will have to again restart if I am to pick a new course. Other than MIT OCW, I haven't been able to find courses freely available in such an organized manner (notes/text + tests + exams). The MIT ocw course was very tough, and I was very demotivated by how much I...

Yes, Kline's book only covers single variate calculus. It is supposed to serve as my first step into learning more math.

Thanks for the reply. The current model we use consists of a system of differential equations, thus the direct motivation towards calculus. Plus, like you said, it is the prerequisite/foundation for other advanced mathematics. But my question is more about my particular method, is it best to...

Hello everyone! I finished a masters in integrative neuroscience about a year back, which was supposed to have a very strong mathematics tilt. Despite this, and the two semesters of mathematics, I feel that it did not help me out much. I ended up doing my masters thesis in a lab of physicists...

I'm not sure how to simplify this without spending a lot of time on it. Is there a pattern that I need to weed out?

Yes, thank you for letting me know. I had issues with a previous thread where I did not give enough information (where I thought I had). Also, since you mention it, I do have a lot of difficulty with identities. I just went back through my notes and realized that I had derived this formula...

It appears that I needed to use $$ \begin{array}{l} \cos ^{2}(\theta)=\frac{1+\cos (2 \theta)}{2} \\ \sin ^{2}(\theta)=\frac{1-\cos (2 \theta)}{2} \end{array} $$ To get the values of cos and sin in the solution. I was not familiar with this formula :nb).

Thank you for your replies. It seems that in trying to post only the relevant parts of the question, I am missing possibly essential information (that I am not picking up myself). The question in its entirety is: Reduce to standard form and graph the curve whose equation is ##x^{2}+4 x y+4...

So I get that: $$ \sin 2 \theta=-\frac{4}{5} $$ $$ \cos 2 \theta=-\frac{3}{5} $$ But what is the next step?

Oh right, I wasn't even thinking about infinity, I was just thinking of it as "undefined" Also, is this also correct? ##\begin{array}{l} \cot 2 \theta=0 \\ \frac{\cos 2 \theta}{\sin 2 \theta}=0 \\ \cos 2 \theta=0 \\ 2 \theta=90 \end{array}##

One of my solutions had this in one part. Why is this the case?

There wasn't a mistake, just one more step was needed: Is there a method to do this division, and how do you get the intuition to divide it anyway? o_O

Oh I see! Using the answers from WolframAlpha gives me the right results. Now to find that mistake! Thank you all!

Oh yes, the ##x_{1}## is supposed to be squared. I tried averaging them but it became very cumbersome

I am simultaneously solving 1) The equation of the hyperbola ##y-y_{1}=\frac{b^{2} x_{1}}{a^{2} y_{1}}\left(x-x_{1}\right)## with the equation of the top asymptote ## bx + ay = 0## 2) The equation of the hyperbola ##y-y_{1}=\frac{b^{2} x_{1}}{a^{2} y_{1}}\left(x-x_{1}\right)## with the...

Summary:: Question: Show that the segment of a tangent to a hyperbola which lies between the asymptotes is bisected at the point of tangency. From what I understand of the solution, I should be getting two values of x for the intersection that should be equivalent but with different signs...

Thank you for your reply. I notice now that not only did I write the equation incorrectly, (wrote ##b^{4} x_{0}## instead of ##b^{4} x^2_{0}##) I incorrectly substituted ##c^2## for ##c## o_O Thank you for your advice, I have this misconception that algebra is unimportant in the computer age...

As part of the final stage of a problem, there is some algebraic manipulation to be done (from the solution manual): But I'm getting lost somewhere: Also a bit of general advice needed: This is part of a self-study Calculus course, and I often have difficulty with bigger algebraic...

Awesome, thank you!

I do not understand how to get ##W = 32r^2##

Yikes! YES, thanks for the catch! I was so frustrated trying to solve this one.

I am unsure how to go about this. I tried following the suggestion blindly and end up with with some cumbersome terms that are not the answer. From what I understand the derivative at each point would equal to T? Answer: I just can seem to get to this. I think I'm there but can't get it in...