Recent content by tangibleLime

Thanks for the help! I got the correct answer, here is my work for any other lost travelers who find this post via Google: (Starting with a+b+2c = 0) [PLAIN]http://mikederoche.com/temp/linalg2.jpg

My apologies, meant to edit that part in but got sidetracked. Here's my work. I take p'(1) = p(2) and solve for a, b and c. I use these new values in a new generic 2-degree polynomial, but what I come up with just looks like a horrible mess. I also noted the answer (from the back of the...

Homework Statement Find a basis of the linear space and thus determine the dimension. q(t) : q'(1)=q(2) Where q is a subset of Q_2: all polynomials of degree less than or equal to 2. I had to change it from p to q so the forum didn't make it a smiley... The Attempt at a Solution...

Hmm, sorry but I have one more question. This problem had two more parts. Part B: In which direction does the temperature increase fastest at P? Part C: Find the maximum rate of increase at P. I was able to calculate part C by simply computing |\nabla T(2,-1,2)|. I thought I knew how to do...

Ah, yes, got it. I was, for the first x in the exponent of e, squaring negative x instead of squaring x and taking the negative of that. Thanks!

Thanks, I knew that was a little fishy. But unfortunately I still can't get the right answer. To get a unit directional vector from those points, this is what I did: P = (2, -1, 2) Q = (3, -3, 3) PQ = (3-2, -3-(-1), 3-2) = <1,-2,1> = v \frac{<1,-2,1>}{\sqrt{1^2+(-2)^2+1^2}} =...

Homework Statement The temperature at a point (x, y, z) is given by the following equation where T is measured in °C and x, y, z in meters. T(x, y, z) = 200e-x2-3y2-9z2 Find the rate of change of temperature at the point P(2, -1, 2) in the direction towards the point (3, -3, 3). Homework...

Homework Statement The sequence a0 -> n is defined by ai = b+i*c. Prove by induction on n that the sum of the terms in the sequence is (n+1)(a0 + an)/2.Homework Equations The Attempt at a Solution I defined predicate P(n) as (n+1)(a0+an)/2. My goal is P(n+1), which is (n+2)(a0+an+1)/2. I...

Ooooh, okay, thanks! Just worked out the whole thing by hand and seems like it flows nicely now. Maybe I made a small mistake before. Thanks again!

Homework Statement Example 3 from this website: http://www.themathpage.com/aprecalc/mathematical-induction.htm Prove this formula for the sum of consecutive cubes: 1³ + 2³ + 3³ + . . . + n³ = (n²(n + 1)²)/4 Homework Equations The Attempt at a Solution I can understand and...

Homework Statement I've been browsing the Internet but can't find a straightforward explanation for a procedure on how to find the image and kernel of a matrix. Question: Find a basis of the image of A, and a basis of the kernel of A. \[ A = \left[ {\begin{array}{ccc} 1 & 2 & 1 \\...

Oh, so I can pick ANY number that makes r(t) equal to the given point?

Actually no, that doesn't work for my problem. (Now I'm doing the actual question I have to solve instead of the book example) Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 1+2sqrt(t) y = t^4 + t z = t^4 - t...

Ooh okay, makes sense. Need to just find the component that makes r(t) equal the given point. Thanks!

Homework Statement Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 2cos(t) y = sin(t) z = t At the point (0,1,pi/2) Homework Equations The Attempt at a Solution r(t) = <2cos(t),sin(t),t> r'(t) = <-2sin(t),cos(t),1>...