What is the angle between the vectors u = <1, 2, 3> and v = <2, -3, -1> ? 213° O 188° O 111° 120°

Q: Find the first three nonzero terms in Maclaurin Series for each function

A: This is a problem related to series expansion. based on the general formula of maclaurin series we…

Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. x + 3y2) dy

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Q: Consider the following equations. f(y) %3D У(5 — у) g(y) = -y

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Q: Describe the domain and range of the function. (x, y) = 9x2 - y Domain: y): x is any real number, y…

A: We need to find domain and range.

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

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Q: Activity 1.5.2. A potato is placed in an oven, and the potato's temperature F (in de- grees…

A: This is a problem related to interpolation of the quantity. Based on the general formula we will…

Q: For each of the following, sketch the region enclosed by the given curves. Decide whether to…

A: In this question we have to find the area.

Q: Find div F and curl F if F(x, y, z) = 3y°z°i – 3x*2°j – 3xy*k. - div F= curl F=

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Q: 1+9n² 1. b) Determine whether the sequence a, =. converges or diverges. If it converges, 1+n² find…

A: 1/infinity=0

Q: (2x – 3y) dx + (2y – 3x) dy

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Q: Find curl (8z i + 9x j + 8y k). curl (8z i + 9x j + 8y k) = ( i )i + ( i )j + ( i )k

A: We know: Where P, Q and R correspond to the components of a given vector field:F→=Pi→+Qj→+Rk→ curl…

Q: What is the second derivative of f(x) 2x-3 2 x+1 10 (x+1)* 10 3 (x+1)° -10x+10 (x+1)* 10x-10 (x+1)*

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Q: dx Ух — 12

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Q: Find the general solution to the ollowing differential equations: (A) y = 2yx(y'+3)+13x %3D

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Q: Suppose that in a memory experiment the rate of memorizing is given by M'(t) = – 0.004t? + 0.4t,…

A: Given,  M'(t)=-0.004t2+0.4t

Q: 1 2 3 1+3* Use substitution to find the Taylor series at x= 0 of the function ... 1 What is the…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 2…

A: Given problem:-

Q: Find T(t) and N(t) at the given point. r(t) = 9 cos(t)i +9 sin(t)j + tk; t = 2 || T(;) N ||

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Q: 5 4 3 2 1 -1 T/2 3T/2 -2 -3 -4 -5 The graph of the function f(x) : given above for the interval x E…

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Q: Solve the following indefinite integrals, using substitution or integration by parts where needed 10…

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Q: Solve by Z method dz 2. 1-2²

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: Explained below

Q: What is the differential equation whose solution represents the family y = Ae3x + Be4x+Cxe4x? O…

A: Given problem:- Find the differential equation whose solution represents the family y=Ae3x +Be-4x…

Q: The graph of f'. 2+ 1- (2,0) -3 4 -3 ±1+ -2+ (-2,-3) (2,-3) 5. The graph of f', the derivative of f…

A: We have to find the value of f(5).

Q: In chapter 10, we will be solving system of equations. Most of the time, we solve system of linear…

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Q: mal places as needed.)

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Q: 2. Write the given (total) area as an integral. a. The area above the x – axis and below y = 4 – x²…

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Q: 5 4 3 1 -1 T/2 3T/2 -2 -3 - -4 -5 The graph of the function f(x) = csc x is given above for the…

A: The graph of the function fx=csc x is given for the interval x∈0, 2π. We have to find one-sided…

Q: If the function f(x) is continuous in the interval [2,8] and f(2)=-7 and f(8) = 9, %3D then which of…

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Q: Determine the vector field of F. F(x, y) = yi – xj

A: Given that,  F(x,y)=yi-xj

Q: Consider the following functions. f(x) 3 Vx - 3 g(x) = x – 3 %3D Sketch the region bounded by the…

A: Let us first find the intersecting point. So,               x-33=x-3⇒x-3=x3-9x2+27x-27⇒x=2, x=3, x=4…

Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: 19. What is the seсond derivative of y бх* - 3x1 + х2 -57 а. у 24х1 — 9х2 + 2х b. у"3 144х — 18 с.…

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Q: d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Describe the graph of the equation. r = 2 sin 10t i + 2 cos 10t j O It is a circle of radius 10 in…

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Q: Show that the differential form in the integral below is exact. Then evaluate the integral. (-2,4, -…

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Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: 1. Suppose you are in charge of payouts for a competitive 10K race. You decide that the top 12…

A: (A) Solution:  In both options total amount is same i.e. $546,000 but option B situation will be…

Q: х2 +7х — 3 (2х + 1) (х dx 2)² —

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Q: 2) Find of the following equation then simplify whenever possible. and dx dx2 x = 1+ Sin t y = Cos?…

A: The given parametric equation,   x=1+sin t, y=cos2t

Q: Consider the matrix 2 -1 A =| 1 3 -1 -2 2

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Q: d Calculate ri(t) · r2(t)] and rı(t) × r2(t)] first by differentiating d dt the product directly and…

A: Given

Q: 2. Find an equation of the plane containing the point P (0,-.) and the line determined by the two…

A: Equation of a plane P containing a line of intersection of two planes P1,P2 is given by, P=P1+λP2

Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+ 5z'yk. ,62 div F= curl F=

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point (2,…

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 - 5t, y = -1…

A: This is a problem related to vector. Based on the general concept and formula we will answer the…

Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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Q: cos(2x)– cosx sin x 4. lim, »o

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