an (4) Let F be ordered field. Prove that the statement Vo: ZX\x6F*XWye FtX &<y)->(<y') is...
Let f and g be differentiable on R such that f(1) = g(1), and f'(x) < '() for all r ER. Prove that f(x) = g(2) for 3 >1.
5.3 Let F be an ordered field, let d > 0, and suppose that d does not have a square root in F. Let F(Vd) denote the set of all a+bvd, with a, b e F, where vd is a square root in some extension field of F (a) Show that F(Va) is a field. (b) Show how to define an ordering on FVa), with vd> 0, such that it becomes an ordered field
Let F be the vector field represented in the figure: y X 1Q0Y, 1X P(-1, 1) X Q3.1 3 Points 2d-Curl F(0,0) > 0 O 2d-Curl F(0,0) = 0 2d-Curl F(0,0) < 0 Q3.2 3 Points OV: F(0,0) > 0 OV: F(0,0) = 0 OV: F(0,0) < 0
(5) Let F be an ordered field, and assume that the statement (Vxe Ft)(3! ye Ft) (y = x) is true. that F has denote by Nx the unique dement of Ftwhace square is x. Prove that of ae Ft and be Ft then na -16 = 9-b We say square roots, and for xe We J Na +ND (D) Let {xn. my be a sequence of points Ft and let bett Assume that {xo la convergent to b. Use...
Let U be an open subset of R". Let f: UCR" ->Rm. (a) Prove that f is continuously differentiable if and only if for each a e U, for eache > 0, there exists o > 0 such that for each xe U, if ||x - a| << ô, then |Df (x) Df(a)| < e.
Problem 7: Let X and Y be two jointly continuous random variables with joint PDF 4 (x y) otherwise a) Find P(0< Y< 1/2 I x-2) b) For what value of A is it true that P(0 < Y < ½ |X> A)-5/16
Let F(x,y,z) = <7x, 5y, 2z > be a vector field. Find the flux of F through surface S. Surface S is that portion of 3x + 5y + 72 = 9 in the first octant. Answer: Finish attempt
Prove: By taking the following problem as being given/true : (Analysis on Metric Spaces) Let f : [0, 1] x [0, 1] + R be defined by f(x,y) = ſi if y=x? if y #r? Show that f is integrable on [0, 1] x [0,1]. Let f : [0, 1] + R be uniformly continuous, so that for every e > 0, there exists 8 >0 such that -y<= f(x) - f(y)< € for every I, Y E (0,1). The...
Is the below statement True or False? The vector field F(x,y) =<xy?, x?y) is conservative. True False
1 xe Let f(x)={? x 8. Prove that f(x) continuous only at +1. Let f(x)= $3.x xs! x >1 Using the definition prove lim f(x)=1 and lim f (x) = 3 x>17 11°