H.W 1.: Use Cayley-Hamilton to find 4 -1 A' and A Where A = [2 1 1 0 1 0 11 2 ]

Q: 44. Let r(1) = (r2, 41 – 3). Find T(t) and N(1), and show that the de- composition of a(1) into…

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Q: 1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( –…

A: Rationalise  all the term and calculate to get the final answer.   Actually as per the barteleby…

Q: "t? + 3) сos(5t) dt 3

A: Given integral is Firstly, we will evaluate the following indefinite integral by parts.

Q: 8. If JM = x+ 17 and MK = 5x – 23, find JL. %3D J M 'K

A: 8 .          J M = x +17           MK =5X -23          Since  JM = MK        ⇒ x + 17 = 5x -23…

Q: A signal x(1) = u(t) €at is applied to a network having an impulse response h(1) = W u(t) e¯ W".…

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Q: Find T(t) and N(t) at the given point. r(t) = 11 cos(t)i + 11 sin(t)j + tk; t= -11 /122 T(5) V122 0,…

A: Given: r(t)=11cos(t)i→+11sin(t)j→+tk→ r'(t)=d11cos(t)dti→+d11sin(t)dtj→+dtdtk→…

Q: 5. Let C be the unit square with diagonal corners at –1- i and 1+i. Evaluate O f(z) dz, where f(z)…

A: Cauchy Integral theorem states that if fz is analytic in a simply connected region D then for any…

Q: If 1 = T T (xyz – 3xy)a, + (zy² + 3x² )a, + xy a,] V(x? + y?) And B = r² a, + sin 0 aø Find |A x B|…

A: Given: B→=r2ar+sinθaϕ It is known that r=x2+y2+z2, θ=tan-1x2+y2z and ϕ=tan-1yx. At P1, 2, 4, obtain…

Q: Show that (A − B )T = AT − B T .

A: Given  (A − B )T = AT − B T

Q: The functions y,(t) = sin(2t), y,(t)= cos(2t) are linearly independent on (-0, x). Select one: OTrue…

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Q: The identity LiS L xyzdzdxdy = "/2 S Sa rsin@cose zdzdrd® x² +y² 1-y² x² +y² is

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Q: e{f; 3et dt } = A(s) A(s) değerini s'e bağlı bulunuz. s =1 için A değerini hesaplayınız.

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Q: 5. (i) Show that +C, 1+u (a) du = 2 In u(1+ u) 1 dx du , using the substitution u = x. (b) J x(1+…

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Q: 10 Suppose z = x + 2i and u=3+ yi where x, y E R. Find the smallest positive value of x z + u for…

A: Given z=x+2i and u=3+yi

Q: 18 Compute r''(t) when r(t) = (t°,9t, cos t). r'(t) = OID

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Q: (b) Now, consider the inhomogeneous problem dre Fre it =F(1,t), 00 00₂ t> 0. w(z,0) = 0, w(0,1)=0,…

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Q: -ALef xe Rbe Such thad Xn→x, show that Yn = xi %3D 4 X.

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Q: 4. Use the I.V.T and Rolle's Theorem/M.V.T to prove that the equation below has a unique solution in…

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Q: 3. Show that the equation for G(r,ø) can be separated by choosing G(r,ø) = R(r)P(ø) into OR Rar ar 1…

A: Introduction: The Laplace equation is one of the most important partial differential equations. It…

Q: 18 In(z – 3) Question 10) Find I = -dz, where C = Iz - 2 + 4i| = 4, Ccw z2 + (4 + 4i)z + 3+ 4i

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Q: X = Ys e %3D (ras.t) %3D (2.1,0)

A: Here we have given u in terms of x,y,z and x,y,z in terms of r,s,t , We use above given relations to…

Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i +4 sin(t)j+tk; t= NG) - ||

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Q: 10.Show that Φ(t) = Ψ(t)Ψ−1(t0), where Φ(t) and Ψ(t) are as defined in this section.

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Q: 4.1 z+ cos(T2) dz, z(z² + 1) with C: |z – i| =.

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Q: 2. A firm produces two goods in pure ompetition & has the pllowing TR & TC functions R= 15Q…

A: In this question, concept of optimization is applied. Optimization Mathematical optimization is the…

Q: (10) Without finding T and N, write a(t) in the forma(t) = a-T + ayÑ at t= r(t) =

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Q: 3. Find an equation of the form y = ab* + c sin (“x) that fits the data below x | 0 1 | 2 |y | 4 |…

A: To find the equation of the form y=abx+csin(π2x) which fits the data  x0123y4111629

Q: N 1 1 202 2{(xn – µ)²}– z(Ord – r). n=1

A: Let y be a function of x and if a is a constant, then we know that ddx(a-x)2= -2(a-x). Here, we need…

Q: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

A: As we know that: The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 (B). From the given integration:…

Q: find: Seas WTT cos Witt dt Sinnt dt findo S

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Q: 12. Let z = æ²y – xy²,x = e " ,y = e#, then which of the following is ? %3D at O a. -2et – 2e-2t O…

A: Partial differentiation of a function is the derivative of the function with respect to one variable…

Q: 1. r(t) = ti + (In cos t)j, -T/2 < t < T/2

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

Q: Find T(t) and N(t) at the given point. π r(t) = 4 cos(t)i + 4 sin(t)j + tk; t = 2 4 1 T(+7) = -√17 Т…

A: given  as you have already found Tangent vector

Q: . Solve the following problems: (a) Utt = 0, 0 0, u (x, 0) = x + sin x, Ut (x, 0) = 0, 0 0.

A: Solution

Q: 6. Write.a.Ct).in. the farm..aaT.T+ a. N. a..r(t).=(tcost). .+ (tsint.) j.+t ..to.

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Q: 2. (a) Determine c, and cz that y = c¿e³x + c2e¯2x + 2 sin x will satisfy the conditions y(0) = 0…

A: We have to determined the value of C1 and C2that y=C1e3x+C2e-2x+2sinx will satisfy the condition…

Q: 1-t? is 1+t2 The differential of u=In, -2 dt 4 -1 A du = O du- 2 dt t4 – 1, B none of the given…

A: Please refer the attached image for complete solution. THANK YOU.

Q: 20 Given that the (bx) +(ay) =(ab), where a and b are constants. Show that-

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Q: (A) Evaluate z dz along from z= 0 to z-4+i along curve of c given by the line from z-0 to z= 2i and…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: x'y=x'+ xy. linear DE Which value of k, the given DE will be homogenous?

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Q: 10 Compute r''(t) when r(t) = (tº,3t, cos r'(t) = %3D

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Y Z H K Given: YX = HX, mZY=mZH, MZZXY=mZKXH Prove: YZ = HK er: AZXY = A by reason

A: Using , Angle - side - angle test,

Q: ZH E LI and HI 1 GJ. Complete the proof that AGIJ S AGHJ.

A: Here we use two concepts  1) sides opposite to equal angles of a.         triangle are equal. 2)…

Q: Suppose r E C[0, 1]. Show that there exists unique y E C[0, 1] such that x(t) = y(t) + 2 5 sin(s +…

A: Consider the provided question,

Q: WD DY because ZX is a perpendicul WX = XY because of Theorem 12-8. Find the value of x to the…

A: Theorem: The perpendicular from the center of a circle to a chord bisects the chord.

Q: Write a in the form of a = a„T+a„N at t = 0 without finding T and N first if r(1)=(2+3¢+ 3¢°)i+(4+…

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Q: Perform the necessary operations to solve the following. Given z1 = 2 + 4i z2 = 5e21 Z3 = 4 cis 40°…

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Q: 1 (aw C. Ifw=f(x.y) and x=1. coso, y=. sino. Prove that

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Q: 2. Which of the following can be differentiated easily without using the Chain Rule? х (b) y = + 2)…

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Q: What values of α and A make y=A cos αt a solution to y′′+3y=0 such that y′(1)=3

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