T 2 If fo)= J* +?dt, use the fundemental theorem of culculus part 1, to find f'cx) fixs=

Q: V. Consider the vector-valued function t² + At – 5 Int Vt, t #1 t2 – 1 Ř(t) = î + ŷ– k, 3i + t = 1.…

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Q: Suppose that r(t) = cos³ t i+ sin³ tj+et k, show that d dr (r.- dt dt d?r X at2 dr d'r. r.at at3…

A: Given: rt=cos3t i+sin3t j+e-t k we have to show that ddtr·drdt×d2rdt2=r·drdt×d3rdt3

Q: Apply runge kutta method of order two on du/dx = sin(xu), u•=0.1,h=0.1 to find u(0,3)

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Q: Prove that fe, r*dx + rydy = 0 where Co is the line segments from (0, 1) to (0,0) by using…

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Q: ди ди ду ду Find the cauchy-riemann equations of, f (z) = | z | sin z. əx' dy'dx' ðy,

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1. In…

Q: For the vector function T(t) = , the arc length function over the interval [a, b] is defined as…

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Q: Let z = e* sin(y+a), show that %3D ôx? oy?

A: Given, z=e-xsiny+a, then we have to show that ∂2z∂x2+∂2z∂y2=0.

Q: Obtain an asymptotic expansion for I(z) = S e-zy°/2 cos y? dy, along [0, 0). as z → 00 -00

A: As per the question we have to find an asymptotic expression for the integral I(z). And we will do…

Q: The integral that represents the length of the curve 7(t) = (t, cos (2t3/2), sin (2t3/2)), where 0st…

A: To represent the integral for the arc length of the curve given by r→(t)=t,cos(2t32),sin(2t32)where…

Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a sin 30 and =7t, where a is…

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Q: Q2) A) Verify that wxy wyx for w x sin y+y sin x +xy. %3D R) Show that f(x v) = e-2y cos 2r…

A: See the details solution in below

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (b) Reparametrize R using…

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Q: Use a scalar line integral to find the length of the curve r(t) = (20 sin , 20 cos ,5), for 0 < t <…

A: Given

Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t > 0. COS So r(t)dt Compute the integral above.

A: ∫0πr(t)dt=∫0π&lt;t,3cos t,3sin t&gt;dt               =∫0πtdt i+∫0π3cos tdt j+∫0π3sintdt k…

Q: find the outward flux of F across the boundary of D.  F = 2xyi + 2yzj + 2xzk D: The cube cut from…

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Q: f(x, y) =(e-2y)Cos2x

A: The Laplace equation is: ∂2f∂x2+∂2f∂y2=0

Q: Find the velocity and acceleration vectors in terms of u, and ug- do r= a(7 - sin 0) and =7, where a…

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Q: Show that the function z = e* sin y satisfies Laplace's equation a²z a?z = 0 дх? ду?

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Q: Compute the principal unit tangent vector at t = T/2. F(t) = sin(2t) î + 2 cos(t) ĵ + tk COS 2 2 - -…

A: unit tangent vector

Q: Use a local linear approximation of the function f(z) = VI cos[(V2r)] at some approximate v3.98…

A: To use local linear approximation of the below function to approximate 3.98cos7.963π. fx=xcos2x3π

Q: Suppose F = ∇ * A, where A = (y + sqrt(z))i + e^(xyz) j + cos(xz) k. Determine the flux of F outward…

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Q: Use the Chain Rule to find az/ðs and ôz/dt. z = arcsin(x – y), x = s² + t?, y = 2 - 2st as az at II

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Q: Bw (s+a)2+w2

A: Ti find the inverse Laplace transform of the function F(s)=Bw(s+a)2+w2

Q: b) Find the laplace trausform of the Runction fCE)= sint.ult - Tt) where u(t-. is a unit function.

A: Here we have use property of Laplace transform when multiplied by shifted unit function.

Q: .a. Compute the divergence of the function (V. v) v = (r? cos?0) î + (r² sin²e)ð + (r sin® cosø)

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Q: Find the Integral of a Vector-Value Function Let 7(t) = (, 3 VE – 2, e ). Evaluate the definite…

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Q: . Compute the tangential and normal components and express the acceleration a in the form a =…

A: The given displacement vector is r(t)=(et cos t)i + (et sin t)j +(2t)k at t=0. The components of the…

Q: Evaluote the live integral | (xZ+ y) ds along the curve c defined byき)=くターも,スセt,-スモ> ON Osts I -21…

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Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a(7 - cos 0) and = 6, where…

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Q: Consider the vector-valued function In(2t + 1) sin t R(t) = î+ t t Redefine (t) such that it is…

A: we say the R(t)  is continuous at t=0  if limt→0 R→(t)= R(0)

Q: Use the Divergence Theorem to evaluate J] F. ds where F (x, y, =) = , and S is the unit S ball x +…

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Q: Find the velocity and acceleration vectors in terms of u, and ug- de r= a(7- sin 0) and =7, where a…

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Q: Using an appropriate linearization, the local linear approximation of f(z)= T+ sin z at 27 is

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Q: B • Write down the integral [F·dī in cylindrical coordinates. F=axy-a,2x F F F coso sino OF -sin cos…

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Q: Consider the 2nd order equation d²y + Sin dy + y? +y = 0. dt, Choose the right assertion A) the…

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Q: Q, Solve he differnktial equntion by Laplace troms form. ý-y =t, yW=1, ý(0) =1

A: Note: According to Company Guidelines we are providing the answer of first question. Kindly post…

Q: Compute the tangential and normal components and express the acceleration a in the form a= arT+aŋN…

A: Calculate the value for aT using the derivative.…

Q: Which of the following represents the arc length of the vector function r(t) = (sin 2t, e, ) on the…

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Q: O If Ret)= t÷1)i+ (t-!)j Find the time Where elocity vechor Normed acceleration vector on

A: Topic- Vector

Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a cos 30 and = 4t, where a…

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Q: find du/dt for u=4ysin(x)+xze^xy^2 and x=3s+t, y=ln(s+t), z=cos(st)

A: The objective is to find  dudt, where u=4ysin(x)+xzexy2, x=3s+t, y=ln(s+t), and z=cos(st)

Q: Use Green's Theorem to evaluate the line integral. e cos(2y) dx - 2e* sin(2y) dy C: x2 + y? = a?

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Q: Find the divergence and curl of F = (e¬* sin y , e¯Y sin z , e-² sin x). %3D

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Q: 2. Find the parametrization of the tangent line to the space curve r(t) = (-t3, In(t), e² ) at t =…

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Q: Given: vector-valued function R(t) whose derivative R' (t) = (4t, 6t, -12t) (b) Reparametrize R…

A: Let's reparameterize vector value function R(t).

Q: Find the integral of ſ r(t) dt for the vector-valued function, r(t) (In(t))i + /1+ cos4t)j + dt k…

A: NOTE: The vector-value function is dependent on variable t, so z component of vector function is…