Mathematical Induction

Prove that the Fibonacci sequence can be obtained by the recurrence relationship. See attached file for full problem description.

Proof of function integrable over [a,b]

Let f: [a,b] mapped onto Reals be a nonnegative function that is integrable over [a,b]. Then the integral from a to b of f = 0 if and only if greatest lower bound of f (I) = 0 for each open interval I in [a,b].

Real Anaylsis

Let f: [a,b] be mapped onto the Reals be a function that is integrable over [a,b] and let g: [a,b] be mapped onto the Reals be a function that agrees with f except at finitely many points. Is g integrable over [a,b]? Why or why not?

Vector analysis

Apply Stroke's theorem to evaluate the integral over C of (ydx + zdy + xdz), where C is the curve of intersection of the unit sphere x^2+y^2+z^2=1 and the plane x+y+z=0, traced anticlockwise viewed from the side of the positive x-axis

Vector analysis

(a) Let F(x,y,z)=(x^2+y-4)i + (3xy)j + (2xy+z^2)k. Evaluate the double integral over S of (curl(F). dS) where S is the surface x^2 + y^2 + z^2 = 16, z >=0 (I) Using Stroke's theorem (II)By direct evaluation (b) Find the flux of the vector field F(x,y,z) = (y-x)i + (x+y)j + y k across the side of the triangle with vert ...continues

Period, amplitude, and viewing rectangle

Determine the period and amplitude of the function.Then describe the viewing rectangle 1-y=3/2cos x/2 2-y=2/3cos pi x/10

Inventory turn over rate/cost

BI:$18,500 (in sales figures)purchases $44,700(at cost)net sales $50,300 (sales figures) markup is 22% based on cost, determine inventory turnover at cost..and at sales price

Real Analysis Proof : Uniformly Continuous

Please see the attached file for the fully formatted problem. Using the definition of "Uniformly Continuous" (attached), prove the following: Prove that any linear function f is (i.e. f(x) = mx + b) is uniformly continuous on R. More generally, if f is differentiable on on an interval I and the derivative f' is bounded on ...continues

Probability distributions

1) Suppose Tucker the beagle is working in customs inspecting passengers and luggage for banned substances, and Tucker alerts the handler by sitting next to the location of the banned substance. What would be a reasonable guess for the distribution of each of the following: (a) the number of alerts by Tucker during the next 3 ...continues

Probability density function

) Let X and Y have joint probability density function f(x,y) (s,t) = ce ^ -(s + 2t) for 0 <= s, and 0 <= t. Find (a) c (b) Pr {min (X, Y) 1/3} (c) Pr {X <= Y} (d) The marginal probability density function of X (e) E [XY] 5) Let X and Y be independent uniform (0,1) random variables. Compute (a) Pr {X < Y} (b) Pr {X ...continues