Evaluate [ xydxc +x²dly if (is the path consisting of the line Segment C From (2, 1) to (4,1) and from (4,1) to (4,5) 5 G F Cis the path described by Xe = 3t-1₁ yeast ² at for 1≤t 45/3

Q: Let M(2t 1; 3t - 2) Show that M is on a line (8) whose cquation is to be determined.

A: We are given : M(2t-1,3t-2) ⇒x =2t-1--(1)⇒y=3t-2---(2) Now, from (1), ⇒t=x+12--(3) Now, from(2) and…

Q: 11. Find F. dr where F(x, y) = (3y, -2x) and C is the path starting at (0,0) to (4,0) to (4,4) back…

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Q: 5.1 Find the upper bound of ez?+1 zp- (z – 1)2 + 5 where C is the circle |z – 1 = 2.

A: We have to find the upper bound of ∫ez2+1z-12+5dz over the circle C such  that z-1=2. Observe that…

Q: 5.- State A for the linear transformation T(ü) = Aŭ %3D - (E) - [-] c+d P 1 a) A = -1 0 1 b) A= |1…

A: We have to find

Q: 11. Suppose that the three numbers r1, r2, and r3 are distinct. Show that the three functions exp…

A: We use definition of wronskian

Q: 2.4 (Ross, 2003, page 593) Show that the relationship $ (x) = x;¢(1;, x) + (1 – x;)ø(0¡, x) is true…

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Q: a) uxx + 2uxy + uyy + Ux – Uy = 0. %3D

A:

Q: Which of the following subsets of R³ are linearly independent? {0} {{} } {O O } S1 S2 S3 6. 2 S4 = 1…

A: To determine which of the following subsets of R3 are linearly independent. S1=112S2=112, 212S3=112,…

Q: Let A = {X € R³ : X and (1, 2, 3), (1, 0, 1) are linearly depedent} Show that A is closed in R³.

A: A={X∈R3:X,(1,2,3),(1,0,−1)are linearly dependent} are same as  A=span{(1,2,3),(1,0,−1)}To show that…

Q: 3.1.11. Let C and C' be cycles in a graph G. Prove that CaC' decomposes into cycles.

A: Let C and C' be cycles in a graph G.  we know that the symmetric difference of C and C' contains…

Q: dz Compute Pc z-1)(z+i)(z-i)' where C is the simple closed path in the following (z-1)(z+i)(z-i) '…

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Q: 12. A linear map T: P (R) → R² satisfies T(x) = (1,-1) and T(1) (1, 2). Find a formula for T(a1x +…

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Q: Consider again the map S € L(P3(R), P3(R)) from the previous problem. Find a basis for range(S). Is…

A: Since the previous problem wasWe will consider the map  as .

Q: 2. - For each map below, either prove that it is linear or demonstrate that it is not linear. (a) T…

A: Consider a map T:U→V is linear if    (i) T(u+v) =T(u)+T(v)   (ii) T(αu )   = αT(u)   , for all u,v…

Q: (0) X. 人セこトン (242) 27 vay 4th 15 where Cis the path from P(0,0 to evaluate つlxe し use Green's…

A:

Q: u? + 5u – 7 If g(u) In(u) find g'(u)

A: The given function,    g(u)=u2+5u-7ln(u)

Q: Consider the following transfer function C(s) s+ 3 R(s) (s + 4)(s + 6) From the information given…

A: The given transfer function is

Q: IF X and Y and So is XXY Path- connected, thun

A:

Q: Question 6: How many different paths in the xyz-space are there from (0,0,0) to (3,4,5) if a path…

A: We have to find the number of paths in the xyz-space from (0.0.0) to (3.4.5) if a path proceeds one…

Q: Consider the following lines. r(t)= (2t+3,3t+2, 3t +4), for - co<t< o0 R(s)= (s+2,4s-2,- 2s+6), for…

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Q: line l1 determined by 2 and ∞ to the hyperbolic line determined by 1 and 3

A: We have two hyperbolic lines  lines l1 determined by 2 and infinity. And line l2 determined by 1 and…

Q: Evaluate fry²dx + x^dy, where C' is the rectangle with vertices (0,0), (4,0), (4,1), and (0,1).

A:

Q: 11. Determine whether the lines L₁ given by x=t, y = 1+ 2t, z = 2 + 3t, (with x < t < oo) and L₂…

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Q: Q4) The linear transformation T is defined by T(x) = 4x . Find a) Ker(T) b) Nullity (7) c) Range(7)…

A: (i) (a) Tx→=Ax→          =5-3111-1xy          =5x-3y, x+y,x-yKerT=x: Tx=05x-3y=0 x+y=0x-y=0∴KerT==ϕ…

Q: 1.2.1. Find the union C₁ UC2 and the intersection C₁ C₂ of the two sets C₁ and C2, where (a) C₁ =…

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Q: Obtain the Bezier curve of order 5 using Bernstein equa

A: We know that general solution for the Bezier curve from Bernstein equation is given as…

Q: 10. The pre-image of P(-1,7) under the mapping x = x - 2y, y=y-2x is? a. (3,-1) c. (1,3) e. none of…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: 5. Find the work done by F eyzi + (xzez + zcos(y)j + (1, 0, 1) +(xyevz + sin(y))k from (1,0,1) to…

A: Answer is mentioned below

Q: Consider the curve 7(t) = (-5+ 2t, 5 + 5t) connecting the points (-5,5) and (-4, 7.5). Compute the…

A: consider the following

Q: 3) show that (N) = ENONP(N,V) = Nop and (N²) – (N)² = Nop(1– p) No N=0+ %3D hint : write N2 = N(N –…

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Q: Example 1.5. Let X = R? x R² and d1 : X R, such that, (1) di(x, y) = d;((r1, 12), (Y1, Y2)) =| ¤1 –…

A:

Q: 2. Suppose n ≥ 1 is an integer. Consider an (n + 1) × (n + 1) grid of integer points; i.e. points of…

A: Consider an (n+1)×(n+1) grid of integers point. That is, points of the form (a,b), where 0≤a,b≤n.A…

Q: 27. Consider the piecewise path which goes along (t,3 – 3t, -t) for 0 <t<1, then along (1,t,-1+ t)…

A: Line Integral along the given parametric curve.

Q: 2.2 Determine whether A. dl between points p₁ (0,0,0) and p2(1,1,1) is path dependent for A = xy² +…

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Q: Show that f10 fdx + gdy = S6 10 5a*y²dx + 2yx³dy is independent of path •(11,–7) ,-10) • (11,–7)…

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Q: . Determine whether the lines.itersect (have a common point) and if so, find the coordinates of that…

A: Given, r(t)=2t+2, 2t+5, 4t+2R(s)=s+1, 3s+2,-3s+5

Q: 9. If t(x,y)(a) is a translation defined by t(x,y)(a,0) = (x+a₂y+ß), determine t(5,8) (2-2)* a.…

A:

Q: 4) a) Two bugs follow the paths r:(t) = and r2(t) = . Determine if their paths cross. If so, at…

A: Any two parametric vector curves cross each other if there exists a parametric value t=t0 such that…

Q: ble. i) s5+2s¹ + 3s³ + 6s² + 6s +9 = 0, is it stable ? s¹+3s³ +7s² + 3s + 6 = 0, is it stable ? ii)

A: Stability of the characteristic equation.If all the roots of the characteristic equation exist to…