I Find for cach of the following. kving your anwer in terms of the parameter t. dr 2, y-M+2 dx-2.y- x= fe, y= 21 Ix4 sin M, y Jen M

Q: · Find fF · dĩ for F = -yi – 4x j+4zk if C is the helix æ = cos t, y = sin t, z = t, for 0 < t < 47

A: Given F→=-yi→-4xj→+4zk→

Q: Consider the following. x = sin(t),    y = csc(t),    0 &lt; t &lt; π/2 (a) Eliminate the…

A: x(t) = sin(t)y(t) =csc(t)

Q: nd the arc length of the parametric curve associated with: t? 4/2 2 3 r (t) = * t3/2, 4t 0 <t< 1. on…

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Q: Let us consider an elliptic PDE is of the form with the condition u + dx? O solve this pof 0 = [u]x…

A: Given equation is, ∂2u∂x2+∂2u∂y2=0...1 u-π2,y=0=u-π2,yux,0=0uy=x,0=e-ncosnx, n∈ℤ Now, apply the…

Q: Given, x(t) -t+3 Draw the 3 s7+ 7è + 7 = (7) A figuezes f (xy4) = In (xy) + x siny / figurees…

A: Solution is given below:

Q: ...-. . Home wurk find Jw * fur the following aud f uuctivus ! て。 - Ł. w = x". sin c %3D coS Cxy -…

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Q: Evaluate F. dr along the curve C if F(x, y) = (x² + y²)¯²(xi+ yj), and C : r(t) = e' sin ti+ e cos…

A:

Q: ds Q. Find Jc 2 + y² + z?" where C is the helix x = a cos t, y = a sin t, z = bt, 0 <t < 1.

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Q: Find the lengths of the curves r(t) = (2 cos t)i + (2 sin t)j + t2k, 0 ≤ t ≤ π&gt;4

A: Given r(t)=2costi+2sintj+2tk We need to find the length of the curvature . The length of the curve…

Q: I Eliminate the ar bi fary constant )- y= Ax+ B sec x 2 2 %3D I. Find the difFCrntial equation +that…

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Q: 5. Do the following tasks using Mathematica. i) Find the length L of the curve y = 1 In a, 1<¤< 2…

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Q: Let I = ,x? cos(x) dx. The approximation of I using the two-point Gaussian quadrature %3D formula…

A: The two point gaussian-quadrature formula  for numerical integration of integral, I=∫abfxdx…

Q: Consider the following parametric curve. Answer parts a and b. x = 4t, y = t°; t= - 1 dy in terms of…

A:

Q: Determine the length of the curve 7(t) = (3t, sin t, cos t) on the interval 0 < t < 2n. %3D А. L =…

A: As we know that, The expression for the length of the vector-valued curve is: L=∫abx't2+y't2+z't2dt…

Q: Find the length of the curve. r(t) (7t, 3 cos t, 3 sin t), -2 sts 2

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Q: Find the length of the spiral c(t) = (t cos t, t sin t) for 0 <t < 2n to three decimal places. Hint:…

A:

Q: Find of the parametric curve x = sect, y = tant, at t = dx? Select one: -3V3 -1 3V3 3y3 1 3v3 O none

A: Here we find the double derivatives value at t=π/3

Q: 10) Find the length of the curve r(t) = (2 sin t, 5t + 1, 2 cos t), -10 ≤ t ≤ 10 $200) il mononut…

A: Introduction: The formula for the length of the curve r(t)=(x(t),y(t),z(t)) is given by,…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: The expression cost is defined for all real numbers t. The expression lnt is defined for all real…

Q: Consider the parametric equations defined by x(t) = 3t² – 3 and y(t)= 2t +1, for t> 0. d'y at t= 1.…

A: Option A is correct option.

Q: Q2/ Find ow/or if w = (x+y+z)³, x=r-s, y = cos(rs), z = sin(r + s) at the point (r, s) = (0,1)

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Q: For the following parametric equation determine dyldx? in the indicated value of the parameter x =…

A: In this question, the concept of the derivative is applied. Derivative We can use a derivative to…

Q: Find the length of the curve r(t) = (3 cos t)i + (3 sin t)j + 2t³/²k , 0sts3. %3D

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Q: Let C be the curve parameterized by Y: [0, b] R³, y(s) = (12 cos(s²), 12 sin(s), 9 s²). Find b>0…

A: The given problem is to find the value of b for which the given length of curve of the given…

Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t) j + 4ln(cos(t)) k,  0 ≤ t ≤ ?/4

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Q: The length of the curve r(t)= [cos(t), sin(t), – 3t]with 0 <t<2n is equal to O A. 2/5 T O B. 2/6 T O…

A:

Q: find dw/ar if w = (x + y + z)?, y = cos(r + s), at the point (r, s)3(1,-1) x = r - s, z = sin(r + s)

A: Given w=(x+y+z)2 x=r-s y=cos(r+s) z=sin(r+s) point (r, s)=(1, -1)   when we differentiate partially…

Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3In(cos(t)) k, 0 stsn/4 Submit Answer

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Q: Find the length of the curve. r(t) = (9t, 3 cos(t), 3 sin(t)), -7<t<7 %3D

A: Given,

Q: Q1: Find the length of the cardioid r= 1 + cos 0 0 < 0 <T

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: II. Draw a sketch of the given arc C and evaluate Sc [(x² − 2y)dx + (2x + y²)dy]. → 1. C is part of…

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Q: Given z = 2 cos t + 23 and y = 5 sin?t dr (i) dt (ii) dt dy (iii) da

A: Explanation of the answer is as follows

Q: For the following, use the information provided to solve the problem. (7) Let w(x, y, z) = xy cos z,…

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Q: Find the length of the curve. A) 18 3 sin(t)+3t, y 3 cos(t), 0 sts B) 6 %3D %3D C) 3T D) 12

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Q: By about how much will ƒ(x, y, z) = ex cos yz change as the point P(x, y, z) moves from the origin a…

A: Given function is Firstly, we will find gradient f at (0,0,0) Now, we will find unit vector along…

Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< t/4

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Q: Q2: Gruph the nector fundion Tt)= Find the equat in for the tanget f functron fexy) = SinCxy) at…

A: a) Given,  rt=cost, sint, t Here  xt=cost,yt=sint,zt=t

Q: - Find the aera under the curve y = cosx Form x = 0 to x = -fx sec² (ax² )dx a#0

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Q: 4) Given: AB is an external tangent to Q0 and 0Q at points A and B, radi for O0 nd OQ are and 12,…

A:

Q: Find the length of the following two-dimensional curve. r(t) (2 cos t+2t sin t,2 sin t- 2t cos t),…

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Q: Find the curve lenght from t=o to te2T of the given curve C: P(E) = (cos3t) î + (sin 3t) Î t ? tJE e…

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Q: Answer! 6. Compute yz dz + zzdy+ zydz along the curve (cos t, sin t, tan t). 0sts*

A: line integrals

Q: z = 2ev-sinx – 3e*cos(y) find: Ве ww m az ,c). ду a2z (n I a2z а) (q-dexp дхду" дудх URGENTTTT!!!!!!

A: Given function is

Q: Evaluate fe kz ds where k is a constant and is the circular helix with parametric equations T = Cos…

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Q: For the following parametric equation determine d'yldx2 in the indicated value of the parameter 37 x…

A:

Q: Find the length of the following two-dimensional curve. 兀 r(t) = (9 cos t + 9t sin t 9 sin t-9t cos…

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Q: Find the length of the curve r(t) = (e* cos t, et sin t , et), – In 4 <t<0.

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Q: Given that the curve C is represented by f(t) = t²i+tj+4k. Find the arc length of C for 0 <t< 2. %3D…

A:

Q: Find the length L of the curve R(t) = 4 cos(5t) i – 4sin(5t) j + tk over the interval [3, 6]. L =…

A: Given:

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.