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Q: EX. Use Euler's method (moditied) t appro y' = x+y for y C1) = 1 ; h =0.1,13XL2 Ư the açcuracy of E…

A: According to the given information it is required to approximate y'=x2+y for y(1)=1, h=0.1, 1≤x≤2

Q: Express dw and ds interms of rand s, where w = x2 + y?x = r – and y = r +.s = 5rand w as = 38 4rsand…

A: topic - derivatives note : As per bartleby guidelines, we are supposed to answer only first question…

Q: Use Jacobi iterative method of following 7+y-z 21+4x+z 15+2x-y x = %3D 4. = Z To find y2, let xo = 0…

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Q: OLet @ = (0,1)n Q = {x€ @104 x<1}. Prove that %3D 2) 2000m

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Q: 00 fcos(x*) dx = ! Ex. 41. Prove that 2 V2 0.

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Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

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Q: Let z 2ev Then: 8z 8z dy sissis

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Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

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Q: Prove: Given that ll Xllo sl1x|1, <vñ lIXloo for XEL". 2 Show that for

A: The matrix p- norm = operator norm                            ||A||p = Maxx≠0 || Ax||p||x||p…

Q: If u =f(x² +2yz, y² + 2zx ).Prove that (v² – zx) + (x² - yz) ди + ди ху

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Q: 4. Given that T : R² → R* and is defined as T(x, y) = (x + a, y + b) . Prove that

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Q: Q4 If f(x, y) = In(x² + y² ) %3D Prove that dy2

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Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: Given F(x, y, z) = (z, x, y) Solve for: а) divF b) curlF

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Q: EX: Verify that z= I+ V3i satis fies the 2. eq.

A: the given equation is z2-z+1=0 given the value of z is z=1+3i2 substitute the value of z in the…

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Q: -2 Let f(t,y) = y + 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1<t<2.…

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Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

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Q: (b) If z =W, show that: x- y xy 0 =

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Q: H.W: if w=√x2 + y2 + z2, x= erCose, yerSine, z=ee prove that aw/ar = e²r/w and aw/00 = e²0/w

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Q: . If x, y E R with x < y, prove that x < tx + (1 – t)y < y for all t e (0,1).

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 4. a) Prove that i) V=I ii) fx+nh = ! I+A 1+A (1) AK fx. = 4k=0

A: Introduction: In numerical analysis, there are many different operators that are used. These…

Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

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Q: Show for R(t) = e?-t and S(x) = 2x + 1, that (Ro S)(x) = e1²+2#.

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Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

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Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

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Q: 7. Prove that if v >-1/2 ; p) = L{xvJ, (; = xı-at-a) H

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Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: For x, y E [0, 1], prove that 1 xy(1 – x – y) < 27

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Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: EX: Find the Z. T. of X(X) = cas wok u(k) Soin

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Q: Verify by direct substitution that Un(x,y)=sinnx sinhny is a solution of Uxx+Uyy=0 for every n&gt;0.

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Q: 2s f( 8ts“, ), (x, 9) = 7xy, and af af ;(x, y) : Assume that w= Find and ds %3|

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Q: Proue that || A|1maπi <j <n 1 Σajl . m

A: In the given question we have to prove that   A1 = max1≤j≤n{∑i=1maij}                         (1)the…

Q: Q3/ prove fry = fyx if f(x,y) = x + xy – 5x³ + In(x2 + 1)

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Q: 4. Prove that (À × B) · (B x T) × (T x A) = [ABT)

A: The objective is to prove that

Q: 3. Show that à = (6xy + z³)î + (3x² – z)ĵ + (3xz2 – y)k is irrotational. Find p such that A Vọ.

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Q: (b) Let z = x + iy = re?". Find |z| and z² first in terms of x and y and then in terms of r and 0.…

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Q: 2. Derive a formula to approximate S* s* f(x;y)dxdy yo xo Using Simpson's rule with x2 – xo = 2h ,…

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Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

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Q: If X is a RV with f(x) = 0, when x 0, P(X 2 a) <u/a. %3D

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Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

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Q: 2. Given z = , show that ху xy(zxx + Zyy) 2 y - x3 x²y? |

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Let flt.v) = v+3t°e'. -2 -y + 3t2e'. Then f satisfies a Lipschitz condition in y with L = 2, given…

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Q: Q/ z = x + f(a) and a = ry. Show that: 尝-端=

A: We use the definition of partial derivatives to prove the given result.

Q: II. Let U = R, { x € R | 26x + 25x = 0}, J = { x €R | |4x + 2| > 10 } and K = { x € R | x? – 3x – 4…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.