Matlab program

Suppose that a rabbit is initially at point (0,100) and a fox is at (0,0). Suppose that the rabbit runs to the right at speed Vr = 5 ft/sec and the fox always runs toward the rabbit at speed Vf = 6 ft/sec. Write a Matlab program that determines to within 1 second, when the fox catches the rabbit. The program should also plot rab ...continues

The one norm

Prove rigorously that ||x + y||1 <= ||x||1 + ||y||1

Local minimum

See Attachment. I have tried substituting integer values of t from 1 to 10 as follows: P(1) = 0.66recurring P(2) = 0.83rec P(3) = 0.75 P(4) = 0.66rec P(5) = 0.83rec P(6) = 1.5 P(7) = 2.916rec P(8) = 5.3rec P(9) = 9 P(10) = 14.16rec Therefore it appears that there are two local minima (at t=1 and t=4)and not exact ...continues

differential equations (analysis)

Let I be an open interval and n be a natural number. Suppose that both f:I->R and g:I->R have n derivatives. Prove that fg:I->R has n derivatives, and we have the following formula called Leibnitz's formula: (fg)^n(x) = the sum as k=0,1,2,...n of(n choose k)f^k(x)g^(n-k)(x) for all x in I. Write the formula out explicitly ...continues

criteria for integrability (analysis)

Define f(x) = x^2 for all x in [0,1]. For each natural number n, compute L(f,Pn) and U(f,Pn), where Pn is the regular partition of [0,1] into n subintervals.Then use the Integrability Criterion to show that the function f:[0,1]->R is integrable. I've already figured out that I can use the sum as k=1,2,3,....n for k^2 = n(n+1) ...continues

criteria for integrability (analysis)

Suppose that the function f:[a,b]->R is integrable and there is a postive number m such that f(x) >= m for all x in [a,b]. Show that the reciprocal function 1/f:[a,b]->R is integrable by proving that for each partition P of the interval [a,b], U(1/f,P) - L(1/f,P) <= 1/m^2[U(f,P) - L(f,P)]

criteria for integrability (analysis)

Suppose the continuous function f:[a,b]->R has the property that: The integral from c to d f<=0 whenever a<=c

Integration

Suppose that the functions g:[a,b]-> R are continuous. Prove that: The integral from a to b of gf <= (the square root of the integral from a to b of g^2) multiplied by (the square root from a to b of f^2) I know that this is called the Cauchy-Schwarz Inequality for integrals. My idea: For each number %(symbol), define ...continues

integration

Note: pi = 3.14...... Prove that (2/pi)x <= sinx <= x if 0 <= x <= pi/2, and use this to prove that: 1 <= the integral from 0 to pi/2 of sinx/x dx <= pi/2

sec.fun.theorem

Note: * = infinite Suppose that the function f:[0,*) -> R is continuous and strictly increasing, and that f:(0,*) -> R is differentiable. Moreover, assume f(0) = 0. Consider the formula: the integral from 0 to x of f + the integral from 0 to f(x) of f^-1 =xf(x) for all x>= 0. How can I provide a geometric interpretation ...continues