Show that the functions f, g : D^1 → D^1, f(x) = x^2 , g(x) = 1/2sin(x) are homotopic, where D^1 is the closed unit disc in E^1 and E^1 is R equipped with euclidean topology.

Q: Q2) a) Find Maclaurin expression of f (x) = Cosh (x) b)Find the gradient of the function f(x, y, z)…

A: Part (a) General form of function fx is Maclaurin series is…

Q: (Q-3) function y=fG. This stretch bu a factor of 3 units. 1) Point (2-3) is a point 15 A gpint…

A: The given function is: y =  f(x) (2, -3) is a point on the given graph.

Q: Q1) Find the canonical form of these question : a) f(x.y,z) =F=x' y' z+x y° z" +x y z b) f(x.y.z)…

A: We are given: f(x,y,z)=F=x'y''z+xy''z''+xyz We are given the standard Form. F=x'y''z+xy''z''+xyz…

Q: Let x, y ∈ R. Suppose x^2 +y^2 = 0. Prove that x = 0 and y = 0.

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Q: Define f(0, 0) in a way that extends f(x,y)=xy[(x^2-y^2)/(x^2+y^2)] to be continuous at the origin

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Q: Let x, y be real numbers such that xy=1x and x≠y. Prove that x^2+y^2≥2\sqrt{2}|x−y|.

A: Given: xy=1x,x≠y To find: x2+y2≥22x-y

Q: [} [2] » 21. Let u = and v = Show that is in k Span {u, v} for all h and k.

A:

Q: 3-) Find the pointls) to point Az(d,0) on x-3~y2 that are closest メ=2 25 +1,5 0.5 + - -ロ5 + 8.5 to…

A: here we have to find the point on the curve x=3-y2 that are closest to point A(1,0) let point is…

Q: In each part, find a function that satisfies the requested conditions. (justify your answer). The…

A: According to the question, I).  The partials exist and the other directionals do not exist.This is…

Q: Write f(z) in the form f(z) = u(x, y) + iv(x, y). a) f (z) = z^3 b) f (z) = 1/z^2

A:

Q: Let g(x) = ax* + bx' + cx + dx + 1 be a polynomium whose graph intersects the points (-2, 4), ( – 1,…

A: We will find out the required solution.

Q: G(x,y)= (x+3y) / (x^2 - y^2 ) Sketch the domain

A: G(x,y) = x + 3yx2 - y2 The denominator cannot be zero. Therefore, x2 - y2 ≠ 0(x+y)(x-y) ≠ 0x ≠ -yx ≠…

Q: #! Find f'cx) if fex)= Čx²+SX+2)(X-)

A:

Q: Examplei Let M be on elliptic parobolbid x= y?4z? a) Find klu) at P= (4, to 12 2. b) Compute the…

A: Given equation of elliptic paraboloid is x=y2+z2              (i) Differentiating x w.r.t y and z…

Q: show that L^1(R) a Banach algebra Commutative

A: We will define the multiplicative operation of Banach algebra in case of L1(R) and prove its…

Q: Prove that the function ((z*)2 Iz| > 0 f (z) = z 0, z = 0 is not analytic at z = 0 by calculating…

A: Given function is f(z)=z*2z, z>00,        z=0 we have to prove, the above function is not…

Q: O Differniate the function after a di fferewt form first rewirming the functio^ * Dont use Product…

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

Q: Finel the ralves of a anel b such that the function aV5-x tb-1 it Hax cos(TT Ix) 9 +1+ b(x²-7)…

A: Note: There is an error in question, for the given function a has 2 values but it cannot be possible…

Q: Find the L^-1 iNVERSE LAPLACE f.) F(S) = 6s/s^2+25 + 3/s^2+25

A:

Q: Prove that the function (z*)2 1리 > 0 0, z = 0 f (z) = is not analytic at z = 0 by calculating all…

A: Calculate the derivative of fz at z=0.  f'0=limZ→0fz-f0z-0       =limZ→0z*2/z-0z-0       =limZ→0z*z2

Q: Let f be the map sending each Comp lex num bey z> Show f(2,Z2) = f (2,) f (2») %3D

A: The detailed solution is as follows below :

Q: Show that at a hyperboic poin, he principall direcions bisect the asymptotic directions using The…

A: Summary:At a hyperbolic point on a surface, the Gaussian curvature is negative, indicating that the…

Q: Let f: R → R such that f (x) = x ^ 2 Analyze if the function is continuous by taking the domain and…

A: Continuous function- Let X and Y be topological spaces. A mapping f:X→Y is said to be continuous if…

Q: Find the linearization L(x,y,z) of the f(x,y,z) = 6sqrtx^3+y^3+z^3 at the point (1,2,3).

A: The linearization of a function f(x,y,z) at a point (a,b,c) is given by the expression;…

Q: (b) Every continuous map S? →T² is homotopic to the constant map.

A:

Q: The magnetic field B due to a small current loop (which is placed at the origin) is called a…

A: Let S be a surface enclosed by the curve C , then ∬ScurlF→⋅dS→=∫CF→⋅dc→

Q: use Euler theorem to show that if f (x, y) is hamog of degree one than x + 0 8 y to fxx (x,y) fyy…

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Q: Find the inverse laplace of ( s + 18 )/( s^2 + s - 6 )

A:

Q: let FCXye+ Siny) f+ (ex+ cos y for pai-) Shoul Hhat F is coserative Vutor Funtion 6) Find a funtion…

A: F is a conservative function iff its curl is 0 that is determined as. Here F is determined to be a…

Q: Find the indicated value for f(x,y) = x^2y^3  fxx(1,2) =  fyy(1,2) =  fxy(1,2) =  really…

A: Given query is to find indicated partial derivative.

Q: Find the Linearizat ion of Non lineah Relations hip Y= (ax+

A: This is the problem of linearization, application of differential calculus.

Q: 3. Let f be a bounded continuous function on C and a E C. Show that f(z) dz lim 0. iz]=r (z – a)²…

A:

Q: Prove that the dual of l' is isometric to 10⁰.

A: Accounting to the given data, prove the given statement:

Q: Sketch the following sets of points in the x-y plane. {(x, x^2): x is in R}

A: