Recent content by Reckoning of Sand

I'm a computer science major. I plan to double in math, but, for a computer science major, would I be better off studying applied math? Right now, I'm not doing as well in my Honors Calculus III course as I have in earlier math classes. (I have a B.) It isn't like anything I did in high...

Then, ##\frac {dy}{dx}=\frac {2}{3}##. And substituting the values for ##y-y_0=a(x-x_0)## gives $$y-1=\frac {2}{3}(x+1).$$

##f(t)## defines ##x## and ##y## implicitly as functions ##x=x(t)## and ##y=y(t)##. To get ##\frac {dy}{dx}##, would I need to define ##y## implicitly as a function ##y=y(x)##?

##f(x_0,y_0)+\nabla f(x,y)\cdot (x-x_0,y-y_0)?##

Homework Statement The equations ##2x^3y+yx^2+t^2=0##, ##x+6+t-1=0## implicitly define a curve $$f(t) = \begin{pmatrix} x(t)\\y(t) \end{pmatrix}$$ that satisfies ##f(1)=\begin{pmatrix} -1\\1 \end{pmatrix}.## Find the tangent line to the curve when ##t=1##. Homework Equations The...

Yeah, I realized that, but it took a while to edit my previous post. Thank you for your help. :) And it all works out when I differentiate my answer! Thanks again.

If I do you use ##i##, then $$x=i \Rightarrow (i)-1 = A((i)^2+1) + (B(i)+C)((i)+1)$$ $$ = A((-1)+1) + (Bi^2+Bi+Ci+C) = (0) + (-B+Bi+Ci+C)= (B+C)i + (C-B).$$ Two complex numbers are equal only if both their real and imaginary parts are equal, so $$Im(i-1) = 1 = B+C = Im((B+C)i + (C-B))...

Okay, if I use that, then $$\frac {x-1}{(x+1)(x^2+1} = \frac {A}{x+1} + \frac {Bx+C}{x^2+1} \Rightarrow x-1 = A(x^2+1) + (Bx+C)(x+1),$$ but won't I still need to use the imaginary number ##i##?

Homework Statement $$\int \frac{x-1}{(x+1)(x^2+1)} dx$$ Homework Equations N/A The Attempt at a Solution I thought that I would use partial fractions, so: $$\frac{x-1}{(x+1)(x^2+1)} = \frac{A}{x+1} + \frac{B}{x^2+1}$$ $$x-1 = A(x^2+1) + B(x+1)$$ ##x=-1 \Rightarrow (-1)-1 = A((-1)^2+1) +...

May I ask what you meant by what "form" I think mathematical induction proofs take?

Ray, I still don't know the answer to your question, but I think I know how to get the answer to the problem. If n = 1, then (A^n)B = B(C^n) becomes (A^1)B = B(C^1) which is AB = BC which is supposed to be true. Assume (A^n)B = B(C^n) is true for n = k. Then (A^k)B = B(C^k) is true...

No. I do not know what induction really is. My instructor only really gave one example quickly. I think he also mentioned that we should have already know what it was, but I did not learn it in AP Calculus BC.

Homework Statement Let A be an nxn matrix, and C be an mxm matrix, and suppose AB = BC. (a) Prove the following by induction: For every n∈ℕ, (A^n)B = B(C^n). What property of matrix multiplication do you need to prove this? Homework Equations The four basic properties of matrix...