Theorem 5.1-1: If X - U(a, b) , then (b – a)° elb ela a + b .2 = 1 2 t + 0, and M(t) %3D 12 t(b — а) 1, t = 0.

Q: Example 3 Find K (t) for the circular helix x= a cos t, y = a sin t, Z = ct where a > 0.

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Q: QUESTION 1 Let E = {qEQ: -n<qs2} then Sup E = and Inf E: %3D %3D %3D For the toolbar, press ALT+F10…

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Q: Given that the characteristic equation has the following roots , what is the complementary solution?…

A: Given are the roots of a characteristic equation    1±3i,1±3i⏟,  2,2,2,2,4⏟       Repeated…

Q: D Question 2 Select all that apply: r y" + 3ry - 2y = In r 3rd order O linear Ononlinear O 2nd order…

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Q: In the figure, ZY = ZX and YZ is produced to T. Prove that YT> XT. Y

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Q: 4) For A= a,āx + azay + a3az, B = b,ax + bzay + b3az, show that %3D %3D A.B cos 0 = A.AVB.B

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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: 1. If XM = 4, XN = 6, and NZ = 9, find XY. %3D %3D %3D 13 If XN 6, XM = 2, and XY = 10, find NZ. M.…

A: observe the figure

Q: If u(x, t) is a solution of u, = uxx * u(x, 0) = 1 + x+ sin (ax) cos (Tx) u(0, t) = 1, u(1, t) = 2.…

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Q: Solve the following problem du = 0 ; x € (0, 1) ,t > 0, u(0, t) = u(1, t) = 0, u(x,0) = %3D %3D

A: Given partial differential equation is, uxx-ut=0       ..............1 With condition u0,t=u1,t=0,…

Q: V, = {2i} m/s V, = {0.448v½i + 0.894v,j} m/s = {5 cos 0 i + 5 sin 0 j} m/s %3D 目。 Vb/r v, = 2 m/s 5…

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Q: iP fca)ex+s and gixjex?-3- find the folllowiny D Rc fext

A: a)         f(f(x))=f(x+5)           =x+5+5           =x+10

Q: 5) roțațion 90° counterclockwise about the origin C ID B.

A: Given query is to perform indicated rotation.

Q: (a) Find the solution to the following Goursat problem: = 4ux, (-2 0), u = arctan(x) on x+2r 0, x…

A: Given: The Goursat problem, utt=4uxx, -2t&lt;x&lt;2t,t&gt;0 u=tan-1x on x+2t=0, x&lt;0 u=xx+3 on…

Q: Let w = a*y cos(4z). Find the following. (a) (x, Y, 2) = (b) (x, Y, z) = ду (c) (x, Y, z) az (d) (2,…

A: In this question we will use basic of calculus i.e concept of partial differentiation. We will…

Q: H.W: if w x2 + y2 + z2, x= e*Cos6, y-erSin0, z=e0 prove that aw/ar= er/w and aw/a0 = e20/w

A: I am going to solve the given problem by using some simple calculus to get the required result of…

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: Question 6. Let u := Vr+ 82, with r:=y+x cost and s := x+y sin t, with t, x, y € R. [6] Determine if…

A: Here we use basic rule of chain rule

Q: Consider the following figure. D F OC = 8 and OE = 4 OE I CD in 00 Given: %3D Find: CD CD =

A: Answer

Q: Suppose that Wi is a standard Brownian motion and consider times 0 < s <t<o∞. Find E[W,W¿] and hence…

A: Given: Wt is a standard Brownian motion  0&lt;s&lt;t&lt;infinity

Q: Question 8 Given the bases B = {u,,u2} and B'= {u'1, u'z} for R², where and u' The transition mat…

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Q: 4 1- cos x+y 4 (x, y)# (0,0) f(x, y) = x+y (x, y) = (0,0) fonksiyonunun fx(x, y) türevinin (0,0)…

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Q: ind c, and c2 so that y(x) = c, sin x+ c2 cos x will satisfy the given conditions. Determine whether…

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Q: 3 (1,3,–1), v = (1,1, 3) vektörlerinin arasındaki 0 açısını belirleyiniz. %3D o arccos() 10 04092 c)…

A: We can find the angle by using the formula: cosθ = ( • ) / (|||| ||||)

Q: QUESTION 5 Evaluate F dr, where F(x,y)=[2y-3cos(x)]i + [4x +6sin(y)]j and C goes counterclockwise…

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Q: Question 1: Let y(r, t) = x'tº + 2x – 3t (a) What is du/az? (b) What is du/a?

A: We have , yx , t = x7 t9 + 2x - 3t We need to find , ∂y∂x and ∂y∂t. We know that , partial…

Q: 1. Find ar, aN, N, T, and k for: (a) F(t) = (5t, t, 4t) at the point (10, 4, 8) (b) ř(t) = (1 – 2t²,…

A: (b) Given rt→=&lt;1-2t2,2-t2,t3&gt; and given point is -1,1,-1. Therefore by comparing, we get…

Q: Given that y1, y2 be a fundamental set of solution to the D. E. (e'y')' + y' + y = 0, x > 0 If the…

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Q: The auxiliary (charasteristic) equation of the DE x²y" + xy' + y = 0 is %3D

A: Euler-Cauchy type differential equation: Let a equation x2y''+y=0 ..(i) Put y=xm in the given…

Q: -3 Let A = -4 -3 -1 9 Define the Lnead teanofamatia T:IR²> IR° by T2)= AR. Find the inages of ů= [oI…

A: Put the value of u and v in the definition of T

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: 13- dy + 2xy = y diferansiyel denkleminin genel çözümü aşağıdakilerden hangisidir? -x* +c1 y = e a)…

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Q: If z=1+y , I= e' cos(s) and y=e' sin(s), then at (t, s) = (1,0) is as O-2e O 2e O 2e

A: if z=x2+y2 where x=et coss , y=et sins then find ∂z∂s at t,s=1,0

Q: Example 10.26. Using Picard's method, find approximate values of y and z corre- sponding to x = 0.1,…

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Q: 25. Evaluate S.(x + Vy) ds where C is given in the accompanying figure. „(1, 1) y = x (y = x² (0, 0)

A: Area enclosed by  these two functions will be Area under the curve  Y=X minus area under the curve…

Q: Given that y1, Y2 be a fundamental set of solution to the D. E. (e*y')' + y' + y = 0, x > 0 If the…

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Q: find c, and c2 so that y(x) = c, sin x+ c2 cos x will satisfy the given conditions. Determine…

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Q: i. y" + 2y' + 16y = cos 3t, yp(0) = ypo, Yp(0) = ypo using your values for ypo & ypo from Part 1.…

A: Given equation is  y''+2y'+16y=cos3t                    (i) Eq. (i) is a second-order…

Q: ),22 %3D Problem I. Given z, = 3el(T76), z, = 2eiT/4), find: 1. Z1 + Z2 2. Z1 - Z2 3. Z,Z2

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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: Question 1 Use the Trapezoidal Rule to approximate e" dr with n = 4. Ar = a ro = b f(ro) = 9 *1 =c…

A: Let's find.

Q: QUESTION 1 Compute [[ ev** where Q is bounded by y = V100-x-z AP 2++ and y = 0.

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Q: ,3 Let w = x'y cos(2z). Find the following. dw (a) (x, y, z) = (b) (x, y, z) = ду (c) (x, y, z) = dz

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Q: The equation (4x-2y+5)dx +(2y²-2x)dy =0 is a lan A Bernoulli's DE B Exact DE C) LDE of order 1 D)…

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Q: 1) Let s,T: e defined by Sx = (0,x1, X2, - ) Tx - (x2,X3, Xyy ..) .. Show that (i) Ilsil = TII = 1.…

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Q: 2 I| ysin(xy)dydx Н.W.

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Q: 11 z- CCW -dz, z2 - z de. c:|2- = sec(u), <ý<.cv Question 11) Find I =

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Q: Find the solution of the following Cauchy problem and sketch its graph att = 0,0.5, 1, 1.5, 2 & 2.5:…

A: Consider the given utt=uxx,              -∞&lt;x&lt;∞, t&gt;0u(x,0)=ϕ(x)=2cosπx4 ,|x|≤20…

Q: Question # 2(Section 15.4 (Green’s Theorem) Verify Green's Theorem by evaluating both integrals ´ƏN…

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Q: Question 1 Write acceleratin a in the form of a = arT +aNN without finding T and N. (a) r(t) =…

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