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Homework Statement I found this algorithm online for computing ln(x). I use the babylonians method for computing square root if it is relevant. fun naturalLog(desired: Double): Double { var naturalLog = desired // desired = x for(number in 0..9) { naturalLog =...

This has been really informative, thank you! I think once I've implemented a properly working algorithm for this, I can move on to implementations of trigonometric functions. Do you have any suggestions on other methods to look at for approximations? For now, I'm not too concerned about...

I uploaded the file here if you're interested: http://www.filedropper.com/spie19991 Not sure why your browser is flagging that site... Loaded for me fine. Proceed at own risk though, lol. Also, back to your original suggestion. I have a question about computing ##e^x## where ##0<x<1##. How do...

This was very informative, thank you. I was well aware of how a pocket hand-held calculator performed operations but did not bother to actually consider implementing their logic(since I'm implementing this calculator as an android app) I will read into both the paper you linked and...

I suppose I could use some tables. I figured if I had a table of ##e^x## I could interpolate up to a certain point. Not sure to what degree though.

Never would have thought that programming would get me more excited to do math! Too cool. I am not too worried about optimization of algorithms for now rather than just getting a proper calculator working. Edit: Ok abck to my original problem. So using the summation I mentioned above I get...

Homework Statement Let's say I want to compute ##2^{2.4134}##. We know that the base is a rational number and the power is an irrational number. Please keep in mind that I have not taken too many math classes yet and I am self-studying right now by making a calculator and respective algorithms...

Let's assume that it was from R4 -> R3. What now? It should never be one-to-one in that case, but can it still be onto?

Homework Statement Say I have a matrix: [3 -2 1] [1 -4 1] [1 1 0] Is this matrix onto? One to one? Homework Equations The Attempt at a Solution I know it's not one to one. In ker(T) there are non trivial solutions to the system. But since I've confirmed there is something in the ker(T)...

Yup! Makes sense now. Just find it interesting that I understand the nullspace and can compute it easily but I still abstract details like that.

The subspace of linear combinations that make your system equal to 0? edit: Now that I think about it, when A is a 3x5 matrix, you need a 5x1 matrix vector X. Since X is 5x1, that means the nullspace is in r5 since X represents all vectors inside the nullspace?

Why would it be in r5 though? Each vector in the nullspace will only have 3 components

Homework Statement If we have a 3x5 matrix: The row space is in r5, the col space is in r3, and the nullspace is in r3 correct? Because you would need 5 components to be a member of r5 so the col space cannot be a member of r5 correct? Here is the question: http://prntscr.com/evo91g...

Oh! That makes this easy then. Is this notation common then? They could have saved me the trouble of typing out a few more characters... :)

Homework Statement http://prntscr.com/eqhh2p http://prntscr.com/eqhhcg Homework Equations The Attempt at a Solution I don't even know what these are, it is not outlined in my textbook. I'm assuming I am is image? But how do you calculate image even? As far as I'm concerned I am has to do...

Homework Statement http://prntscr.com/ej0akz Homework Equations The Attempt at a Solution I know there are three problems in one here, but they are all of the same nature. I don't understand how this is enough information to find out if they are subspaces. It's all really abstract to me. I...

No, because they are multiples of one another So, in hte first set they are linear independent. But because set two has all vectors adding several multiples of each member it is linear dependent(hope this makes sense)? I didn't see that the second set had four members and not three. This makes...

So if you could make a combination that indicates that they are dependent then it would mean that it depends on values of the vectors? I'm having a hard time putting this all into perspective without examples. How do you know this? I thought they were just 3, individually independent vectors...

Homework Statement Homework Equations The Attempt at a Solution if there exists a set with 3 vectors, and all of them are linear independent, then by definition no linear combination of the 3 vectors can equal to 0. I believe that's an accurate definition right? So in this case, the...

So projecting PoP on to N gives a vector that is parallel to n essentially correct? And this vector represents QP?

Homework Statement assuming the point given is P(3,2,3) and the equation of the plane is 2x + y + 2z = 2, find the distance and the point Q which represents that point Homework Equations The Attempt at a Solution Okay so I think that OQ-OP = QP, which connects the two points and is the line...

Hi guys, I'm coming back to this problem and I wanted to know why h can't be 4 in this scenario. Is it because the second row will be 0,0? Why does that make this not a unique solution?

So in the second matrix, since it is a diagonal with non-zero numbers and no variables being free, it is consistent with a unique solution as every variable can be pointed to a specific value(Hope that makes sense)? And in the first matrix, there is a free variable. If there is a free...

Homework Statement Consider the following matrix where * indicates an arbitrary number and a ■ indicates a non zero number. http://prntscr.com/e4xqkx [■ * * * * | *] [0 ■ * * 0 |* ] [0 0 ■ * * | *] [0 0 0 0 ■ | *] (Sorry for poorly formatted matrix. The link above contains a screenshot...

Yeah this makes a lot more sense now. I didn't understand what made rows linear independent, I wish my textbook had gone over this. I was wondering why it had to be h that couldn't be 4, and not k but this clarifies that.

Just a question - does k still have to correspond to what h is(it should right - because it would be inconsistent otherwise)? Its bothering me that I can't algebraically find specific, unique values. What if h was 3? -y = k - 4 - > would k have to be 3?

##\begin{bmatrix} 1 & 2 & | & 2 \\ 2 & h & | & k \end{bmatrix}## ##\begin{bmatrix} 1 & 2 & | & 2 \\ 0 & h-4 & | & k-4 \end{bmatrix}## ##\begin{bmatrix} 1 & 2 & | & 2 \\ 0 & 1 & | & (k-4)/(h-4) \end{bmatrix}## ##\begin{bmatrix} 1 & 0 & | & 2 - ((2k-8)(h-4)) \\ 0 & 1 & | & (k-4)/(h-4)...

hmm... how about x = (2h-2k)/h and y = k/h. Do i just choose random values?>

I have not seen such a theorem before. But I'm having troubles drawing the connections here - I believe that the two rows must be independent of each other, but they also need to be consistent. How does rank play into this? If it is of rank 2, then they will have two rows/columns that are...

for row reduced echelon form i got: x = (2h-2-k)/h y = (2+k)/h I believe rank indicates the linearly independent columns in a matrix, in this case rank 2? Do I just input values for h and k so that x = 1 and y = 1?

the determinant is h-4 correct? how does this help me?

http://prntscr.com/e4kqrc i'm assuming 2x + hy = k, sorry

hmm.. I'm unsure of how to make an augmented matrix in latex. it's meant to be : row one: 1x + 2y = 2 row two: 2x + h = k

Homework Statement $$ A = \begin{bmatrix} 1 & 2\\ 2 & h\\ = k \end{bmatrix} $$ Mod note: Corrected augmented matrix: ##\begin{bmatrix} 1 & 2 & | & 2 \\ 2 & h & | & k \end{bmatrix}## Homework Equations The Attempt at a Solution Ok, so apparently it's a bad idea...

If it is the same, then that's enough for me to know. Thanks!

I was asking why is it that lim u-> 0 f(u)/u = lim x -> 0 f(x)/x in the last step of the solution.

Homework Statement I'm trying hard to understand as my professor hasn't taught(nor does my textbook) on how this works. It is known that $$\lim_{x \to 0}\frac{f(x)}{x} = -\frac12$$ Solve $$\lim_{x \to 1}\frac{f(x^3-1)}{x-1}.$$ Homework Equations The Attempt at a Solution OK.. so I do this...

Since c is an element of x,y then it can't be larger than 0.5 or smaller than 0? And as such this proves that since 48|y-x| will be greater since y is greater than c? So the side with c will always be smaller.

I forgot to add that they are differentiable on the interval (x,y)

Homework Statement Suppose that x,y are in (0,0.5). Show that: $$\left|\frac{1}{x^3}-\frac{1}{y^3}\right| ≥ 48|x-y|$$ Homework Equations The Attempt at a Solution I think that we need a function ##f(t) = t^{-3}## & ##f'(t) = -3t^{-4}##. Now we use the MVT here to show that there is some c...

Homework Statement $$\int_{0}^{2} r\sqrt{5-\sqrt{4-r^2}} dr$$ Homework Equations The Attempt at a Solution would i substitute ##u=4-r^2##? After of which I would input into the integral and get: $$\int_{0}^{2} \sqrt{5-\sqrt{u}}du$$ What would I do here? Do I just work inside the radical(so...

Yeah this is all the information I have. I forgot that L'hopitals can only be used if indeterminate form is found. Yeah you're right. Sorry about that i'll edit it Are you saying that x should be equal to f'(1)?

Homework Statement Problem 1: ##f'(1) = -2## Solve: $$\lim_{x\to0} \frac{f(e^{5x} - x^2) - f(1)}{x}$$ Homework Equations The Attempt at a Solution Okay so these type of problems really get to me. I'm going to assume some level of substitution are needed but I'm really unsure. I'm guessing...

using these properties would I get something like this?(after splitting the left side): ##3\int_{-1}^{3} f(x)dx - a\int_{-1}^{3} g(x)dx + \int_{-1}^{3} adx## ?

Homework Statement ##\int_{-1}^{3} f(x) dx = -4 = \int_{-1}^{3} 2g(x)dx## Now find a value(constant a) that makes the following true: ##\int_{-1}^{3} [3f(x) - ag(x) +a] dx = \int_{-1}^{3}(1-ax)dx## Homework Equations The Attempt at a Solution I'm unsure if my approach here is correct but I...

After a bit of googling I came up with a solution I think it's right(very different from the jibberish i had in OP) but I'm not sure. I did the solution on mywhiteboard as this seems very tedious to do on mathjax. http://prntscr.com/dchmps After a second look that looks messy. Sorry about...

Homework Statement http://prntscr.com/dcfe0u Homework Equations The Attempt at a Solution So I'm not really strong in proofs but I think you may be able to do something like this: $$lnL = \frac{ln(1+1/x)}{x}$$ $$lnL = \frac{1/x^2}{1+1/x}$$ and then more simplifying I get something like...

Homework Statement http://prntscr.com/daze68 What I don't understand: 1. "P be a polynomial with degree n" do these equations satisfy this description?: $$p(x) = (x^2 + x)^n$$ $$p(x) = (5x^2 + 2x)^n$$ etc. 2. "C1 is a curve defined by y=p(x)" c1 is essentially just the curve of the...

Realized my mistakes were because I wasnt' careful enough Okay so h(2) = 1.6m as 4-2(1.2) = 1.6 then we can use that to find x(2): √(25-1.6^2) = 4.7377 And then i input these values in to: $$2(4.73)*\frac{dx}{dt}=2(1.6)(1.2)$$ $$\frac{dx}{dt} = \frac{3.84}{2(4.737)}$$ and i get 0.405 for...

h(2) = 1.6m and x(2) = 4.73? Is my initial approach wrong though? And why is it that I got $$\frac{dx}{dt} = -1.6$$ which is the same coefficient of h(2)? I get that from a logical perspective this problem is very easy but I still want to do the math behind it.