9:51 R² x=(x)) ва налів P 1 g(x) = (0,0) kit homotopy from fto homotopy from of g to

Q: Find Domain and Range Sove all points without leavin ℗ x + y² + Z 2 X+ 4+=+/-5 +2Z 3 Sin(x+3y) +2…

A: Domain is the set of points where function is defined. And range is set of images of function.

Q: 1- iz If z = x +iy and w =- z-i show that w = 1= zis purely real

A: Use modulus property

Q: 1. Let f(x) = { **sin²³1/x ifx #0 0 if x=0. (a) Prove that 0 is a local minimum point for f. (b)…

A:

Q: EVALUATE THE FT. 3 1) S (x³ +1) Inx dx 2.) Sxe ²x dx 3.) S dy √y + 4√√y³ 73

A: We have to evaluate the given indefinite integrals.According to our guidelines we can solve only 3…

Q: (a) A function p(x) with domain (0,8) that has p' (x) > 0 everywhere, p" (x) = 0 for all æ 4. 4 2 4…

A: Given domain of p(x) is 0,8.

Q: Show that f(r) = O(|x – xo|*) and g(x) = o(]x – roP) imply f. g(x) = o(|x – xo]k+i). - -

A:

Q: Q3: Prove that X, = X, = ,X; = y %3D %3D %3D are symmetries of ys y"=3y" y"2+y''3 %3|

A: Given: To prove that the  X1 = ∂∂y,   X2 = ∂∂x,  X3 = y ∂∂ x are symmetries of  y' 5 y''' = 3 y' 4…

Q: t f(x+y)=f(x)+f(y) + 2xy-1 for all real x and y and f(x) be a differentiable function. [f f^ prime…

A:

Q: Find the centroid of the region lying underneath the graph of the function f(x) = (x² + 64) over [0,…

A: Find the centroid of the region lying under the graph of fx=x2+64-12 over 0, 7. Formula: The…

Q: Let o be the hypercube [0, 1]". For any f e C[0, 1] show that (). (x1 + x2 + + Xn dxjdx2 dxn = f ...…

A:

Q: prove that 01a| = 0 => a=o @ 1-al-lal @lak b ⇒-b<a<b @la-bla lal-lb/

A:

Q: a) Get the (2n+1)x Pn (x) = (n +1) Prar tx) +o Pau (x) reconnection polynomials using the; P(x, 2)=…

A:

Q: # ∙1.) (Cauchy form f defined f(n) exists (i) For each (ii) for of some. on and Taylor Thm) (a, b)…

A: 1) Suppose that  is  defined  on     Also  given that    exists  and  continuous  on  c)  We  have…

Q: -1-3x+ e3X ) im x>0 hint: L'Hopitals Rule - cos(x)

A:

Q: Prove that if m is a positive interger, l'(-m+) = 1.3.5..(2m -1)

A:

Q: Orthonormalize [1, t, t²} in P₂(R) with (p, q) = p(0)q(0) + p(1)q(1) +p(2)q(2) }

A:

Q: 5. Prove or (a) f: R² → R, f(x, y) = x² + y disprove: f is invertible. (b) f: R→ R², f(x) = (x,x+2)

A:

Q: Find дх (дхду) 6,e at the point(7,), where g(x,y) = cos(y) [sen(x) + xy].

A:

Q: K=Zp(t) ,then f(x)=x^p-t is irreducible over K[x]

A: GIVEN: K = Zp(t)

Q: (LO16) Find all of the zeros of f (x) = x³ – 4x² + 2x + 4. A) x = 2, x = 1 ± i C) x = 2,x = 1+ V3 B)…

A: If you like the solution then please give it a thumbs up.. The Answer is:       x=2,x=1±3 So, Option…

Q: x -4x +5 - Prove that: f' x x-2

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 5 Thass [[1(², 3)dA = [² [² fff(x, 0 1 drdo

A: Given that the function fr,θ=4rcosθ+rsinθ. Find the value of given integral.          The formula…

Q: az Find for z = x'y'eV

A:

Q: 1 Assume that 1 < a < b_and equation is solvable. + x = Show that this * – b'

A:

Q: Q4 A) Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: The objective of the question is to verify the hypothesis of the Cauchy Picard theorem for the given…

Q: F. (x) = (1) following Theo-pm by , indaction (1リ Prove The using Eqwatio, Theoranm, For um be-…

A:

Q: If z=xtiy where x and y are real, find the real and imaginary parts of:- Z-1 Z+1 ピージ (x+アア 2.xy…

A:

Q: Q2: 2 xy"+y' +=y= x³ 3 X

A:

Q: Let f and g be functions defined by f (x) = 1+x +ex-2x and g(x) = x4 – 6.5x² + 6x + 2. Let R and S…

A: Consider the two regions R and S enclosed by the graphs of the given functions as shown in the…

Q: (a)

A: Option B- a reflection across the line y = x, followed by a dilation centered at the origin with a…

Q: Calculate the divergence of cach of the following functions (a) r²î + y²§ + 2²k. (b) yzî + xzj+ xyk.…

A: As per the instruction, we will answer only the first 3 subparts. For (a), For a given vector fx, y,…

Q: Ex L: =)(co(ax) – 7sin(3 x)) FC<). gC<)dx Let V be the vectar real valued function of all continous…

A: An inner product space is a function from a vector space to another vector space. There are certain…

Q: 1.)(x + y - 1) * d * x - (x + 4y + 2) dy = 0

A:

Q: (b) Let n, m be positive integers. Define a function (2zm + 3)"e-3z sin?(z) h(z) = zm+2n cos3 (z)…

A: We will use definition of argument principle