write a in the form a = aTT + aNN at t = 0without finding T and N. r(t) = (2 + 3t + 3t2)i + (4t + 4t2)j - (6 cos t)k

Q: Which of the followings are true? I. D1000 re (2 - 1000)e IL D2021 cos(5a) = -52021 sin(5a) III.…

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Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian. b. Establish…

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Q: 3 e flow in the field F = 4i + 9j + 2k along the path C, where C is the curve r(t) = 7 cos 4ti + 7…

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Q: Compute r"(t) and r(t) for the following function. r(t) = (cos 2t, sin 3t, cos 6t)

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Q: Use a Fourier sine expansion to solve ĉu ô’u ôt ôx? u(0,t) = u(1,1) =0,1> 0, = x sint in (0,1) ×…

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Q: Let 7(t) = (- 5t² + 5, 5e 5t, 5 sin(4t)). Find )dt (don't include the +C) + C

A: Given: r→t=-5t2+5, 5e-5t, 5sin4t

Q: write a in the form a = aTT + aNN at the givenvalue of t without finding T and N. r(t) = (et cos t)i…

A: Given: The given vector equation is r(t) = (et cos t)i + ( et sin t) j + √2 et k,   t = 0    Formula…

Q: Uxr + 3uyy = cos(x + y)u is second order, non linear, non homogeneous first order, linear,…

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Q: Let 7 (t) = < - 2 cos(2t), Find F(t)dt (don't include the +C)

A: Please refer to the image below.

Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

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Q: a/ Find laplaee t ransferm Halt-r) cos(t– T) Co. 1

A: We will use the formula of Laplace transform to find the required value.

Q: Find i (t), given 7(t) = (5 cos(– 2t + 3), 4te', – 2t In( – t)). %3D F (t) =

A: To find the derivative of the given parametric vector, we need to differentiate each component of…

Q: Find z(t) for X(s) = 8-2 %3D $(s+ 1)(+9) Select one: O a.z(t)3D-86(0) + 금etu(e)-뷰.e 2.cos3t. u(t) +…

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Q: b. g(b) Use the Substitution Formula, f(g(x)) • g'(x) dx = f(u) du where g(x) = u, to evaluate the…

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Q: 9. Let r = 3 sin tî + 3 cos tj + 4tk. Calculate N

A: Given r(t) To find N(t)------ unit tangent vector

Q: Exercise 15. Let f(z) cos z (z2-1)2 The residue off(z) at zo = 1 is a) – sin 1 b) sin1cos 1 c) -(sin…

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Q: Compute r"(t) and r""(t) for the following function. r(t) = (cos 4t, sin 2t, cos s 6t)

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Q: Let 1973 - sinh(1/(2z)) and : (0, 27]→C, Then, (t) = 3 cos(t) - 13 sin(t) %3D 2Ep1070 1971 |F(z)dz =…

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Q: C) Find a z and of xy" ay (xy2) - -군3 COs %3D

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Q: Let 7(t) : - Find (don't include the +C) V

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Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

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Q: Evaluates t cos(2t*) dt

A: here we will put 2t4 = u then solve further

Q: de B: Evaluate the 2m a-cos20 when z = et and Iz| = 1. %3D

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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: Find r(t) that satisfies the initial condition(s) r″(t) = −4 cos tj − 3 sin tk,    r′(0) = 3k,…

A: Given r″(t) = −4 cos tj − 3 sin tk,    r′(0) = 3k,    r(0) = 4j

Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (5 e' cos…

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Q: In Exercises 1 and 2, write a in the form a = a tT + a nN without finding T and N. 1. r(t) = (a cos…

A: Consider the position vector

Q: Let 7(t) = (V4t + 4, ,sin(4t) 4t -1' From F(t)dt (don't include the +C) Find

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Q: 3. Evaluate the following: cos1(t)dt C. dx b. J Jezx-1 In(x)dx V1-t2 a.

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Q: B. Switch the order of integration: cos (x2) dædy. Just SET UP with the order switched. DO NOT…

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Q: Let C be defined by 7(t) = |cos (t), sin (2t), t²| for 0 < t < n 2 sin(Vz) 9x*dx + 2zdy + + 2y ) dz…

A: Using the result that  ∫cF·dr=∫cPdx+Qdy+Rdz=∫P(r→(t))dxdt+Q(r→(t))dydt+R(r→(t))dzdt dt Here,…

Q: Determine DFT X[ej"] of the signal (answer a or b) a) x[n]coswon. b) x(n) = a"u(-n- 1) %3D

A: As it's mentioned in the question to answer between a) or b), so showing steps for only one part. b)…

Q: Use a computer algebra system to evaluate (x2 – 2xy) dS. (Round your answer to two decimal places.)…

A: Here we solve the given calculus problem.

Q: Solve the equation Uxa + Uyy = 0, 0<x<™, y E R Up (0, y) = Uz(T, y) = 0, y E R Uy (x, 0) = h(x), u…

A: let us solve above equation in Fourier series form let us consider the given equation  uxx+uyy=0 let…

Q: (a) Prove that dv 1 2 u? + v2 arctan u- + C. 2 u 2, /2/2 ru (b) Prove that I dv du 2 - u? + v2 18 by…

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Q: Represent f(x, y) (0<x < 2, 0 < y < 4) by a double Fourier series пту f (x, u) = EBin Ssin () sin…

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Q: Condsider the ODE z (1) +5 ( (1) +6z (t)- F(t) where the forcing function is given by the Fourier…

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Q: Compute r" (t) and r"(t) for the following function. r(t) = (cos 3t, sin 6t, cos 2t)

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Q: Let A E R²x2 be special orthogonal. Show that there exists & E [0,27t) such that COS O - sin o A =…

A: According to question,Given Matrix,A = cos ϑ-sin ϑsin ϑcos ϑ

Q: Find the convolution of f(t)=cos(t)f(t)=cos(t) and g(t)=cos(2t)

A: Given function is f(t)=cos(t) and g(t)=cos(2t)

Q: Express Q(x) = cos4 (x )+ 12 as the composition of three func-tions; that is, identify f, g, and h…

A: Q(x) = cos4 (x )+ 12 We need to express the given function as a composition of three functions  that…

Q: 5. Use the Chain Rule to find dw dt where w = sin 12x cos 4y, x=7, and y =t". :- dw (Type an…

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Q: In Exercises 1 and 2, write a in the form a = aTT + aNN without finding T and N.1. r(t) = (a cos t)i…

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Q: Let f(r, y, z) = In(x² + 2) + y?e - cos(2y2). Find feyr-.

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Q: Suppose w = In(æ² + y² + z²) , Compute dw/du and dw/dv in two different ways: ue3" sin(9v) , y :…

A: GIvenw=ln(x2+y2+z2) where x=ue3vsin(9v) , y=ue3vcos9v and z=ue3vTo find∂w∂u and ∂w∂v

Q: Use the Chain Rule to find az/as and az/at. (Enter your answer only in terms of s and t.) z = sin(0)…

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Q: Vrite a in the form a = a-T+anN at the given value of t without finding T and N. r(t) = (– 2t + 3)i…

A: Introduction: The tangential component of acceleration is given by, aT=v.a||v|| The normal component…

Q: write a in the form a = att +ann at the given value without finding T and N r(t) =(2t+4)i+(t)j…

A: Given, r(t) = (2t+4)i + tj +t2 k, t = -1 and we have to calculate the form a = aTT + aNN at the…

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.