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Hi I am trying to decipher solve linear ODE using an integrating factor and have fallen at the first hurdle! Following the example given I am trying to write the DE in standard form. The example given is: Solve xy'-y=x^2 I follow that: y'-y/x=x however don't follow the next step being...

Im trying to find the local min and max and saddle points of this equation f(x,y) = x^4 + y^4 -4xy +1 and the only issue i have right now is with the critical points i have found the partial derivatives for fx and fy which are fx = 4(x^3-y) and fy = 4y^3 - 4x when i set them to zero and...

It deals with implicit differentiation. I am having trouble understanding the final part of the problem dealing with exponents. I was asked to find \frac{d^2y}{dx^2} for x^4 + y^4 = 16. My work: 4x^3 + 4y^3 \cdot \frac{dy}{dx} = 0 4y^3 \cdot \frac{dy}{dx} = -4x^3 \frac{dy}{dx} =...

Is there any major advantage to defining the natural numbers as starting at 1 rather than starting at 0? If so, what is that advantage and where does it come into play? Or is it more a matter of taste or tradition?

As a disclaimer, I'd like to say that I'm not sure if this belongs in the stat or the pre-Calculus sub-thread... For an essay I picked my topic to be on Olympic weightlifting, (I figured since it was based all around numbers it would be relatively easy to talk about) and right now I'm having a...

(This isn't homework exactly, since it's not for a class, but it is definitely a problem from a textbook.) For some generic direction vector r = xi + yj + zk, the text book states that the div r = 3 and that grad r = r/r. (the vector is actually the position vector in the electric field given by...

hi i have an issue: a and b are real numbers 1-check that (a+b)^2-2ab=a^2+b^2 2-if a+b=2√3 and a*b=-2 calculate: a-b a^2+b^2 a b i have already solved it but the problem is i used the quadric formula to find b and we didn't learn that at school and a and b have 2 values (0.50402... and...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 2.2 on free modules and need help with the proof of Corollary 2.2.4. Corollary 2.2.4 and its proof read as follows: In the second last paragraph of Bland's proof above we read: " ... ... If...

I need help understanding why the solution set #35 shows -4x changing from negative to positive. In my mind the -4x should have remained negative in line 2. Line three also confuses me. Shouldn't +5+4 be +5-4? 35) h(x)=-x^2 - 4x + 5 h(x)=-(x^2+4x) + 5 H(x)=-(x^2+4x+4)+5+4...

I am hoping that someone will be able to help me with this problem. I don't understand why the solution shows h(x) going from h(x)=-x^2-4x+5 to h(x)=x^2 +4x+5. It seems to me that it should have been h(x)=-(x^2-4x)+5. Why is the added 4 positive in line three? If I add 4 to the solution then...

Indefinite Integral: (x-1)/(x2-4x+5) I approached the problem by first completing the square( I got (x-2)2 +4)in the denominator, then pulling out the (1/4) and proceeding with partial fractions. Yet the answer I get is : (1/4) * ln(x-2) * arctan Obviously an error on my part. The answer...

I have tried these problems over and over and I can't seem to get them right. They are: 4sin(y^2)+x^-5=e^6y and ((-6x^2)/(y^4))=7 I normally make it to tutoring sessions, but I was assigned these problems last minute and there are no tutoring sessions between now and when they are due...

Hello, Could any one help me with following question; From Vx =K/R2 where Vx isthe Voltage at sensor x, R is the separation & K is a constant. I get to R1 = x2+ y2 aR1 = (R –x)2 + y2 bR1 = x2+ (R – y)2 Where a = V1/ V2 and b = V1 / V3 I’d like to find x, y and R1 in...

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i was solving a calculus problem and i yielded the answers 1/sqrt(5) and 2/sqrt(5). when i looked at the solution in the book it showed the answer as (1/5)*sqrt(5) and (2/5)*sqrt(5). I checked it with my calculator and it shows that my answers and the book's answers are equal, but I cannot...

Hi, a simple but puzzeling problem (at least to me). What i have is an alphabet of size 6 : \Sigma = \{a,b,c,d,e,f\} What I am looking at are 4-touples (a,b,c,d)_{1}, (a,a,a,a)_{2}, .... (...)_{|\Sigma|^{4}} Basically there are 4 different 4-touple classes: a,a,a,a -> all characters are the...

Issue with Eigenvectors [solved] I put my problem in the pdf document since matrices are tedious in latex...I am trying to find eigenvectors for a linear system, I can produce the same eigenvalues given by wolfram (see pic of wolfram results)...but I cannot get the same eigenvectors and I...

I ran into another rationalizing problem and it is messing me up. it is f(x) = 1/sqrtx so when I take my f(a+h) - f(a) I get {[1/sqrt(x+h)] - [1/sqrtx]}/h but inlike the question before that dealt with indeterminate form I am finding rationalizing is getting a bit messy. I end up with...

trouble starting a proof So the claim is: If X^3+4X>0, then 5x+9>6 We are supposed to show our scratch work which generally means he wants us to figure it out algebraicly and then use our work backwards to form the proof. However, i'm not sure how to start. We don't have any theorems that...

I'm not sure if I just hit my limit for the day regarding Calc, but I may have. I was wondering if someone could take a look at this problem for me. I have the solution in front of me, with most of the steps, but I don't see how to go from the last step to the conclusion. The problem is...