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...
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...
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...
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}##
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
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...
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...