Show that F (x, y) = x2 + 3y is not uniformly continuous on the whole plane. Hint: You must prove that there are pairs of points, arbitrarily close together, on which the variation of F is large, for example, (n, 0) and (n + 1/n, 0).

Q: Q12: If x + y = 10, then the largest possible Q13:The absolute maximum value of A) has no absolute…

A: Since, we have been asked to solve question-(13) in which our aimis to find the absolute maximum…

Q: Let f: [2, 7] → [0, ∞) be continuous in [2, 7] a (2,7). Then prove that there exists at least one…

A:

Q: P 2. ( a) Find the average value of f on [9,25]. b) Find all c in [9, 25] such that f(c) = favg.…

A:

Q: Let's assume that f(x)= r²+c* I c-16 g(x, a) = a* x² + ar Find a such that the following error is…

A: Given that where            That is  Also, given that

Q: [1+2p(x-1)+(x-1)² x≤1 x>1 [qx+p -) -) Find the values of q, in terms of p, for which fis continuous…

A: Given:f be a function defined by:a. To find the value of q in terms of p, for which f is…

Q: If f is continuous on the interval (-0,00) and f"(x)=3¯*(x- 14) (x– 5)100 , then f(x) has inflection…

A:

Q: = √x + 2,-2 ≤ x ≤2 ax²-bx, x+1 x-2 ) 2 3

A: Topic:- calculus

Q: Show that the function f(x): = √/x² is uniformly continuous ON A:= [1,00), but that it is not…

A: To show that f(x) is uniformly continuous on A, we use definition of uniform continuity and to show…

Q: Could you write a proof for the following: Suppose F: X → Y is one-to-one. Prove that for all…

A:

Q: Let f be continuous on an interval I from a to b with only one critical number c in (a, b). If f'(c)…

A: Step 1: Step 2: Step 3: Step 4:

Q: Show that in R with the usual topology, the only open sets connected by trajectories are the open…

A: Given that R with the usual topology  A collection of of subsets of R which can be expressed as a…

Q: 4. Prove fx=x2+4 is not uniformly continuous on R

A:

Q: If the ratio of boys to girls in tennis camp is 3:5 if there are 64 campers, how many are girls 

A: We find out how many girls as follows:  • We first need to determine the total number of parts in…

Q: 15) Prove that if ffx) is continuous at x=0 then so is V f(x) provided that fix) zo for all x in the…

A: Step 1: Step 2: Step 3: Step 4:

Q: Prove f(x) = x2+4 is not uniformly continuous on R.

A:

Q: V = M2x2 (R) let M = { A€ V A = A²} N = { A = V A = -A ² } Subset of the vector space V V = MON…

A:

Q: 1. If f(x) is bounded on [a,b], then f f(x) may not exist. Prove this statement theoretically or…

A:

Q: Consider the function f(x, y) = x^2 − y^2 over the square centered at 0 whose length of each side is…

A:

Q: Let's assume that f(1) = 1² + c* I c=14 g(z, a) = a* z²+a*z Find a such that the following error is…

A:

Q: Let f(x)=1/x. Show that f is bounded from above on any interval (α,1), where α>0, but the function…

A:

Q: (b) Show that xE R, x2 - 4x + 5 > 0.

A: As this is a multiple question type, only first question is to be solved, according to the Bartleby…

Q: Let f: A→ B, where A= {1,-1}, B= {1,2,3}, and f(x)= 3×x²+2, find Range إجابتك * Codomain إجابك * Is…

A:

Q: Prove: f(x) = 1+x² is Lipschitz continuous in R.

A: Step 1: Step 2: Step 3: Step 4:

Q: Letf(x) be defined for all x>0 and be continuous. Let f(x) satisfy f =Ax)-fy) for all x, y and f(e)…

A:

Q: Let i, j, k e Za and w, x, y e Zb with i, j, k all different from each other and w, x, y all…

A: Let the number of elements in the domain be equal to m, and the number of elements in Zb be equal to…

Q: Let f(x) =x²-3X²- 24 x +26 a) the open intervals on which flx) is incheas in g aN the open intervals…

A:

Q: f(x)=x+10x+25 x+5 3 O True is continuous at x = -5 O False

A: