Q2) homeomorphism. Prove or disprove: The function f: (R, T1) - (R, 13) defined by f(x) = 3x is a %3!

Q: Suppose that f(x, y) = at which %3D - {(x, y) | 3 < x < 4, 3 < y < 5}.

A: we have ,  f(x,y)=xy at which (x,y)|3≤x≤4,3≤y≤5 we have to calculate,  ∫∫Df(x,y)dxdy

Q: (a) Let f(x) = tanx- 2, g(x) = x5 + x³ and h(x) = Vcsc5x. Then find %3D the f(g(h(x))), using chain…

A:

Q: Suppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. Prove that…

A: Solution is given below:

Q: f X1, Y1, are two positive unequal numbers and Xp = (Xn- 1+ Yn– 1) and Prove that the sequences (xn)…

A:

Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

A:

Q: If f(x, y, z) = excosy + z, show that fxx + fyy + fzz = 0

A:

Q: Q3/ 1- Let f: Zn → Z10 define by f(x) = 2x+2. Is fhomomorphism or not, explain your answer.

A: Given :-  let f : ℤn → ℤ10 define by f x = 2x + 2.  To Determine :-  Is f homomorphism or not.

Q: Verify that fy = fx, for the function f(x,y) = x° + 3y° +7. 9 For the function f(x,y)=x° + 3y° +7,…

A: The given function is fx,y=x9+3y9+7. Evaluate fx as follows. fx=∂∂xx9+3y9+7fx=9x8 Thus, fx=9x8.…

Q: Find the linearization L(x) of f(x) at x = a. f («) — 4а? + 2а — 3, а — -5 -

A:

Q: Verify that fxy = fyx for the following funtion.  f(x,y) = ex + y + 1 fxy = ? fyx = ?

A: Given,            fx,y=ex+y+1

Q: Find the critical numbers of the function f(z) = z2 - z / Answer (separate by commas): z =

A: Solve the given problem.

Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)

A:

Q: Show that the function f (x, y)=(2 + x-y) / [1+ 2x ^ 2)+(3y ^ 2)] ∈R has a limit at (0,0).

A: I have provided a solution in step2.

Q: Show that the function f(x, y) x4 + y? has no limit as (x, y) approaches (0,0).

A: Note: Since we can solve at most one problem at a time, we have solved the first one. Kindly…

Q: Define the function f(x, v) = 4x³-x³y-4y5 3x5-3y5 at the origin so that it becomes continuous there.

A: A function is said to be continuous at (a,b) if the the value of function at (a,b) is equal to…

Q: Let F = &lt;5x^2, 2(x+y)^2, 9(x+y+z)^2&gt; Find divF (divergence)

A: First of all, consider the vector F and find F1, F2, and F3.

Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given, the function f(x, y) = 5x – 10y + y3, we have to show that the function is differential by…

Q: Use the comparison theorem with f(x) = = 1 √x to show that [₂²= 1 √x-1 is divergent.

A: See this solution in below

Q: Find the linearization L(x) of f(x) at x=a f(x)= x+1/x a=3 show all work

A:

Q: lim, - f{x)= 0, then f(x)dx diverges Select one: O True False

A: When the limit exist or equal to 0 then the series is convergent otherwise divergent.

Q: (b). Show that iff= u+iv is analytic in a region S and u is a constant function (i.e., independent…

A:

Q: Find the limit of function f (x, y)D. at the point (0,0) through the path x=y². а. О b. 1 8 d. does…

A:

Q: b. Test the continuity of the following function 1, x< 0 V1-x, 0sxs1 ,atx 0,1 x- 2, x21

A: We have to check the continuity of f(x) at x=0, 1

Q: of of and ду For the function f(x,y) = In (7x + 9y), find

A: The given function,     f(x,y)=ln7x+9y

Q: Show that the limit of the function f(x,y) = at (0,0) does not exist. (x+y)² x² + y²

A: Limit of a Function: Like a single-variable function, a multi-variable function can also have limit.…

Q: attached

A: Linearization of f(x) at x=a is given by

Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: Find a and b so that the function S4z - 3x² + 4, z -2 is both continuous and differentiable. a = b =

A:

Q: Q2. Show that F(x) = 3 – x², x € is contractive on its domain, but does not have any fixed points.…

A: To show - Show that Fx = 3 - x2, x ∈ -14, 14 is contractive on its domain, but does not have any…

Q: Q3/ 1- Let f: Z, → Z10 define by f(x) = 2x+2. Is fhomomorphism or not, explain your %3D answer.

A:

Q: 4. Give an example of a continuous function f : (0, 1) → R that cannot be uniformly approximated by…

A:

Q: Show that there does not exist a function f(x, y) such that VJ= (y2,x). Hint: Use Clairaut's Theorem…

A:

Q: Q = find of るf and るこ for the Ganction f(xz)-ディズ メ+Z

A:

Q: If F(t) = 2xyi + xyz2j + ex+yk, then what is the divergence of F? Select one: A. 2yi + xz2j + ex+yk…

A: The divergence of a vector F=P,Q,R is given by div F=∂P∂x+∂Q∂y+∂R∂z. The given vector is Ft=2xy…

Q: If F = (x²)i + (2x²y)-(3-2)k find div f curl f at (1,-1, 1).

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose that f : R →R is continuous and that its image f(R) is bounded. Prove that there is a…

A:

Q: Use the comparison theorem with f(x) = = 1 √x r∞ 1 •√₂ √I-1 to show that is divergent.

A: Solution is given below:

Q: Find aland U so that the function S 7z³ – 3x² + 7, z -2 is both continuous and differentiable. al =

A: To Determine: fins a and b so that the function is continuous and differentiable given: we have a…

Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

A:

Q: Show that f (a) = is Libschitz function on r+ 2

A:

Q: Prove that the limit of xy[(x^2 - y^2)/(x^2 + y^2)] is zero as (x, y) goes to (0,0)

A:

Q: Show that the function f(x, y) xy? – 1 has y – 1 no limit as (r, y) → (1, 1).

A:

Q: Find the Wronskian for the set of functions.{x, −sin x}

A: Given:  f(x1)=x and f(x2)=(-sinx ) The wronskian is given by the following determinant:

Q: Show that f (x, y) = has no limit as (x, y)→(0,0) Vx2+y2

A: The objective is to show that f(x,y) has no limit as (x,y) approaches to (0,0).

Q: Q1// Find and sketch the Domain of f(x,y) In (x' y)

A:

Q: 2. Use the Intermediate Value Theorem to prove that the equation e* = 4 - x³is solvable on the…

A:

Q: 1. Estimate the limit of the signum function s(x) as x approaches zero from the right. (-1, x0

A:

Q: Determine local extremum f(x,g) = xy(4-x-). %3D

A:

Q: Suppose that the function f: R → Ris continuous and that its image f (R) is bounded. Prove that…

A:

Q: 2. Show that the function. 5x²³²Bin 12 F(x)= โ x2 0 (x=0) is not of bounded variation on [1,1].…

A: