Recent content by andyk23

y(0)=1/2

Find the solution y = φ(t) of the given problem and evaluate φ(t) at t = 0.1, 0.2, 0.3, and 0.4. 1.y'=3+t-y y = φ(t)=t-2e^-t y(1)= 0+(0-2e^0)*(.1)=.8 and the correct answer is 1.19516 2. y'=2y-1 What I'm getting stuck on is do I use the formula y(n)=y(n-1)+f(t(n-1),y(n-1)h because...

I'm just having a trouble showing, \frac{k(k+2)}{k+1} + \sqrt{1+\frac{1}{(k+1)^2}+\frac{1}{(k+2)^2}}\ = \frac{k+1(k+1+2)}{k+1}\

I'm just having a trouble showing, \frac{k(k+2)}{k+1} + \sqrt{1+\frac{1}{(k+1)^2}+\frac{1}{(k+2)^2}}+\sum_{i=1}^{k}\sqrt{1+\frac{1}{i^2}+\frac{1}{(1+i)^2}}\ . = [itex]\frac{k+1(k+1+2)}{k+1}\ .[itex]

I'm just having a trouble showing, \frac{k(k+2)}{k+1} + \sqrt{1+\frac{1}{(k+1)^2}+\frac{1}{(k+2)^2}}\ . = \frac{k+1(k+1)}{k+1+2}\ .

Yes I meant that!

yes sorry about that!

1. Homework Statement ∑ i=1 to n1+(1/i2)+(1/(1+i)2)−−−−−−−−−−−−−−−−−−−−√ = n(n+2)/n+1 2. The attempt at a solution First I did the base case of p(1) showing 3/2 on the LHS equals the 3/2 on the RHS. Then I assumed p(k) and wrote out the formula with k in it. Then prove p(k+1)= p(k)+...

Sorry I had it written down on my paper but I didn't type it right! I'm just having a brain freeze on what I need to multiply the other rationals to have a denominator of (k+2)^2. Assuming that's the correct next step.

Sorry I'm not following.. I understand what you're saying I did, just confused on which part I did the (a+b)^2 = a^2 + b^2

Homework Statement \sum i=1 to n\sqrt{1+(1/i^2)+(1/(1+i)^2)} = n(n+2)/n+1 2. The attempt at a solution First I did the base case of p(1) showing 3/2 on the LHS equals the 3/2 on the RHS. Then I assumed p(k) and wrote out the formula with k in it. Then prove p(k+1)= p(k)+...

Vector field F(bar)= <6x+2y,2x+5y> fx(x,y)= 6x+2y fy(x,y)= 2x+5y f(x,y)= 3x^2+2xy+g(y) fy(x,y)=2x+g'(y) 2x+g'(y)= 2x+5y g'(y)= 5y g(y)= 5/2*y^2 f(x,y)=3x^2+2xy+(5/2)y^2 Then find the \int F(bar)*dr(bar) along curve C t^2i+t^3j, 0<t<1 I'm stuck on finding the last part for the F(bar)...

\int xy^3 dx+ x^5 dy, where C is the rectangle with vertices (0,0), (4,0), (4,2), and (0,2) F(bar)= <P,Q> <xy^3, x^5> derivative of P with respect to y= 3xy^2 derivative of Q with respect to x= 5x^4 Double \int (5x^4-3xy^2) dx dy with limits for x from (0,2) and y limits (0,4) I get 0 for...

Let f : P3 → M2x2 be given by f(a + bx + cx^2 + dx^3) = (a + d 0) (0 b − c) 1. Determine the nullspace and nullity of f and specify a basis for the nullspace. -I came up with N(h)= {a+bx+cx^2+dx^3/ a+d=0 & b-c=0}= ={( 0 b), a,d are elements of R} ( c 0) 2. Determine...

A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: z=90 p^.5 r^0.5 Chemical P costs $400 a unit and chemical R costs $3,200 a unit. The company wants to produce as many units of chemical Z as possible with a total...