Write a in the form a = arT + aN N at t-0 for R(t) = t?i + (t +); + (t - }c")k

Q: Derive and use the estimate 800 |u (x, t)| < 1 -7²t/10 re (2k + 1)* k=0

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Q: Calculate F. dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

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Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: Evaluate the integral (2 + 6) (2? + 6z + 2)*dz by making the substitution u = x² + 6x + 2. + C

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Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: 10e dz by residue theorem, where C is the contour |2| = 2 Je 1z4 +5z3 Evaluate

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Q: Use Cramer's rule to solve for r' and y in terms of x and y: y = 31' – 2y

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Q: Find length of the cardioid r-a03from 0 0 to 0 t %3D

A: To find Length of cardioid r=aθ3  where θ=0 to θ=π

Q: Use Gramer's Rule to Find K,y and Z -y-2Z = -8 + 32 = 2 %3D 7X +y+Z = o

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

Q: T: R2 R2 is defined by х + 7х, [3x, – 4x2] X1 %3D and B = {u,,u,} and B' = {v,v,}, where %3D -- --…

A: Given transformation T:R2→R2, defined by Tx1x2=x1+7x23x1-4x2 and B=u1, u2 and B'=v1,v2 Here u1=22,…

Q: Let f (x, y) = 9e2xy what is fryx (x,y) =? %3D

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Q: Enter the function In standard form. y = 2(x-1)(x +5) The standard fom of y = 2(x-1)(x +5) is

A: y=2(x-1)(x+5) first multiply (x-1)(x+5) =&gt;(x-1)(x+5) =&gt;(x^2 +5x -x -5) =&gt;(x^2 +4x-5)

Q: t-4 - Given s(t) find s'(t)- t+3

A: st=t2-4t+3 take derivative s'(t)=ddtt2-4t+3 use the quotient rule fg'=f '·g-g'·fg2

Q: Find the d. c. of T from definition.

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Q: Show that Plx-1,y) = A(x, y) X+ y-1

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Q: At time t hours a company is selling items at a rate of r(1) items per hour. 10 Interpret the…

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Q: 4) Suppose that T : R³ → R² is defined by T((x, y, z)) = (1+2x – z , 3 – x + 6y) Is T linear?…

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Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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Q: This question is from partial differential equation please sir g give me answer immediately

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Q: Let f(x ,y, z) = x²yª + z³ and x = 4s?, y = 2st?, and z = 3s?t. %3D %3D

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Q: Oo Find a functiom f and a nunber a E(4,7) such that I+/" f(t) dt = tan x a number a c(#,) Cost

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

Q: af Find for f(x,y) = e* In(x + 7y). %3D ду 7. -7 e*(x +7y) e*(x +7y) 7(x+7y) 7(x+7y)

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Q: IT Evaluate v if y=xsinx at x = 6.

A: Giveny=xsinx

Q: Q1:- Let T =- where W-N(0, 1) and V~xShow that T2-F(1,r).

A: We know that  The ratio of chi-square divided by its degrees of freedom is called the…

Q: Q2/ Show that {1,cosx, sinx,cos2x, sinx,...} Form an orthogonal set on [-Tt,t] *

A: A set of vector B is orthogonal if every vector in the set is orthogonal. Therefore, the dot product…

Q: af Find the ar I and iff (x,y) = x² - xy, x = r² + s and y =r - s² as

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Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: 1. Use calculus to identify the absolute extreme values of ƒ (x, y) = y³ — 3xy + x³ on the triangle…

A: Given function is fx,y=y3−3xy+x3. We have to identify the absolute value of fx,y on the triangle…

Q: LZHP - DTNV. Complete the statement below. ZZ = _2_

A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

Q: sWhat are the points of discontinuity? (x+1Xx-5) y3D *+4x+3 Ox-3, x--1 Ox--3, x=-1 Ox=5 Ox=5,x=-1

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Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

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Q: 4) Lett =,u = x? - y² ,v = 4xy³. Find %3D ax ду

A: t=uv

Q: H.W. a PDE from the followi'ng- @u=f() Form メツ 0u=fcx?ー)

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Q: Compule bethan eact aud numecild Velore 123_3/117-48)* 17E57) to use the odler hat@ for derikate to…

A: solving part (a):

Q: Compute the discriminant D(x, y) of the function. f(x, y) = x³ + y4 - 6x-2y² + 2 (Express numbers in…

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Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…

Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…

Q: Additional Problem Prove the statement: 3X CZ such that Vx E X, 2 | x and 3 | x.

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Q: =Xtanx dk, Prove that ="IH (n+1)I,+(n-1) -1 T 1 2 n

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Q: O show thet fu) =2a +3b is Candin Uous where a, b are Constants.

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Q: O Consider K points x1,..., X € C. Show that 0;x; € C, for >0; = 1,0; e R i=1 i=1

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Find the cemplex fourth routs of Z: 2 J3-22

A: Given, z= 2√3-2i Therefore, r= √[(2√3)²+(2)²] r= √(12+4) r= 4 θ= tan-1(-2/2√3) θ= -30°

Q: ди n. = 3 Ôx? para t> 0, 0<x < 3 ди ди (0,1) = (3,t) = 0 u(x,0) = 3x +1

A: Solution

Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: Show that the dyfferential equatian IS exact x(スt5in t) do + cast -2tu) abe +x² dt-

A: We will show that the given differential equation is exact.

Q: Solve Utt - c?uxx = 0, –n 0, %3D u(x, 0) = f(x), u(-n, t) = 0 = u(n, t), ux(-n, t) = 0 = ux(n, t).

A: Given: The PDE is utt-c2uxx=0 , -π&lt;x&lt;π,t&gt;0.

Q: 13.2 鄭28

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Q: Find the are length of f(r) = (r + 3)2 from r = 0 to x = c in terms of c. %3D 2/3

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