Recent content by CalculusSandwich

Find the smallest positive integer which when divided by 12, by 17, by 45 or by 70 gives a remainder of 4 in each case. I know I can approach this problem by writing the equivalence classes. x=4mod12 x=4mod17 x=4mod45 or x=4mod70 I also know I can find x by multiplying 12*17*45 + 4...

not quite what you did was forget to subtract e^ (-t/50) from e^0. ${fave} =\int _{0}^{38}e^{u}(-50)du $ is evaluates to e^ (-38/50) - e ^0 which is something like -.54 times your constant which was -78*50/38 gives you a positive number, somewhere around 55. add that to ${fave}...

Ok I'm confused here. Thanks for the replies, but yes Ivy I meant the Augmented matrix AX=B is written in matrix form and row reduced. You say that there will be a rows of 0's, but there won't because B is the solution set, so won't it just be the square matrix if A is a 3x2 and b is a 3x1? Am i...

So it states: The Equation Ax=b has a solution if and only if b is a linear combination of the columns of A. That means the columns of A are linearly dependent. So then if I have a matrix A and a vector B, and after row reduction on Ax=B i get, the identity matrix. So does that imply...

This is an application of the chain rule.. You can multiply the inner product and get...[x^3-3x^2] ... now you bring the 1/3 out in front and reduce it by 1 as by application of the derivative. 1/3-1/1 = -2/3 So you get what 1/3[d/dx[x^3-3x^2]]^-2/3 so then it's: 1/3[x^2*(x-3)]^(-2/3) *...

I'm sorry there's not. That's just the next step to solving the integral. then i take the dot product of <4v-v^3, 2u+v, v^2 + 4 - v^2 > dot <0, 2v,1 > I get < 0, 4uv + 2v^2, v^2 -v^2 + 4 > which simplifies into 2v^2 + 4uv + 4 so i integrate between... \int 0 to 2 and \int 0 to 4...

anyone?

Homework Statement calculate the upward flux of f(x,y,z) = <yz,2x+y,y^2+z> Let S be the portion of the cylinder z=4-y^2 lying in the first octant to the right of the plane y=4. a parametrization into the u v plane is:r(u,v)=(u,v,4-v^2) region is a rectangle in the uv plane with bounds, (0,0) ...

Correct you write your matrix in terms of the free variable which in this case would be x1. So [1,0,0,0] would be the solution set. Also if this is an augmented matrix the general solution would be inconsistent since, 0x1 + 0x2 + 0x3 = 1, cannot be true.

Ok so my question was: The directions state: Find the solution space of the following systems of linear homogeneous equations: x-y+z-w=0 2x+y-z+2w=0 2y+3z+w=0 Is the same as finding the solutions, because I did that and got (-z, -3z, 3z, z). So i said the solution space is...

the same was as you would any number x^3 * x^2 = X^5 So e^(x+2) * e^(-x) = (x+2-x) or e^2, correct?

I have the problem 3e^(x+2) = e^(-x) and I need to find X. It's been a while since I've looked at any Calculus 2 stuff so I am not sure on what to do here. I take the natural log of both sides LN(3e^(x+2) =LN(e^(-x))= (x+2)ln3e = -xlne So (x+2)Ln3e= -x Where do I go from here?

Thanks for the reply's I got it, for the 2nd problem I get e^-6 which is believe is right. Great replies ty.

Ok, so I have the problem lim n-> infinity (1 +5/n)^(4n) So looking at it without trying anything I can see for n arbitrarily large 5/n goes to 0. That means (1+0)^(infinity). One to the power of any real number is one. However by looking at the definition of e as x->infinity I can say (1+...

Thanks for the replies, I applied the ratio test. 7^K+1+1 2^3k-1 7^k (x) 7^2 2^3k (x) 2^-1 --------- x ---------- = ----------------- x -------------- 2^3k-1+1 7^k+1 2^3k 7^k (x) 7^1...