2. Given the vectors à = (a₁, a₂, a3) and b=(b₁,b₂, b3) show that a × b = -b xã.

Q: Find the values of x, y and z that correspond to the critical point of the function: f(x, y) = 4x² +…

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Q: 1. A 6 kg sign is suspended by two strings making angles with the ceiling as shown in the diagram.…

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Q: 2. Which expression represents the volume of the rectangular prism shown? 2x - 3 a) (2x - 3) + (3x +…

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Q: (a) Find an affine change of coordinates that takes the unit square with vertices in the uv-plane to…

A: (a) The vertices of uv-plane is given as , P*=0,0 , Q*=1,0 , R*=0,1 , S*=1,1 and the vertices of…

Q: Determine the infinite limit: O -∞ O 8 7-x lim x 4 x² - 2x - 8

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Q: The cross product is anti-commutative. This means that axb=-bxa. Show this is true for a=(2,3,4), b…

A: Given  a→=2,3,4 and b→=-5,-4,-3. We have to show that  a→×b→ = -b→×a→.

Q: Determine the general solution of xdy + ydx = 0 A xy=c B) xy^2 = c y=c (D) X=C

A: Given Problem:- xdy+ydx=0 Find General equation  of given differential equation

Q: 2. Which graph is NOT a function? a) b) 20.00 0.00 0.00 c) n 20.00 x X d) 10

A: Option D  is not a function.  Because to qualify as a function, for every value of "x" there must be…

Q: Find the following limit. lim

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Q: Suppose that f(x, y) = 5, and D = {(x, y) | x² + y² ≤ 1}. Then the double integral of f(x, y) over D…

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Q: Find the arc length (s) of the curve r(t) = (est, -2e5t, 3e5t) for 0 ≤ t ≤ In (2) 8=

A: The arc length s of the curve r→t=x(t), y(t), z(t) for a≤t≤b is given by s = ∫abx'(t)2+y'(t)2+z'(t)2…

Q: 2. Compare the rates of growth of f(x) = x + sinx and g(x) = x as x approaches infinity. f(x) grows…

A: The given functions are fx=x+sinx and gx=x we have to compare the rate of growth as x approaches to…

Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 6y² + 6z² and x…

A: To evaluate the triple integral ∬∫ExdV where E is the solid bounded by the paraboloid…

Q: Determine the radius and interval of convergence of the following power series. k X ()* 12 M8 k=1…

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Q: 5 Find the derivative of f(x) = -4√x + T8 Type your answer without fractional or negative exponents.…

A: To find the derivative of the given function.

Q: 2. (xy + x) dx = (x²y² + x² + y² + 1)dy

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Q: The annual rainfall in a certain country varies from 0 to 9 inches and is a random variable with…

A: It is given that the probability density function for the annual rainfall value is given by below…

Q: Evaluate the Integral using the following values. [°x³ dx = 260, [°x dx = 10, [°dx = 2 [°(22-7x-x²)…

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Q: Exercises: Use the theorems on limits to evaluate each of the following, if it exists. 1. lim (2x³…

A: See this solution in below.

Q: 9x²-4 :) Tax² ² (x² − 4)(x²+4) dx

A: Topic:- application of integration

Q: Find the arc length of the curve on the interval. r(t) = (3 sin(t), 7t, 3 cos(t)), 0 ≤ t ≤ The…

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Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

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Q: Find the curvature of the curve r(t) = (-1-4t, 2-t, 4 - 4t) at the point t = - 1. Check Answer

A: We know that curvature of a curve is given as: k=||r'(t)×r''(t)||||r'(t)||3

Q: Evaluate the following integral over the Region R. (Answer accurate to 4 significant places). SS R…

A: In this question, we need to evaluate the given integral.

Q: Find the second derivative of the vector-valued function r(t) = (4t+ 3 sin(t))i + (5t + 3 cos (t))…

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Q: esc Consider the vector field F = O The vector field is not conservative O The vector field is…

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Q: Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check…

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Q: Evaluate (2 - xy) ds where C is the curve given below. -2 -1 -2

A: Given   ∫C2-xyds Curve C

Q: Use following series > k=1 the (+48 integral test Converge. to decide if th

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

Q: -) 1 = dx x (1-√x)²

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Q: f(x) 3. What does lim = 0 show? X→∞ g(x) O g(x) grows faster than f(x) as x goes to infinity. Of(x)…

A: The given limit is limx→∞fxgx=0

Q: (a) As an iterated integral, with limits of integration A = B = C = D= Suppose f(x, y, z) = E = F=…

A: Let's evaluate triple Integral.

Q: Answer: Use a triple integral to find the volume of the solid enclosed by the paraboloids y = x² +…

A: Let's find volume by using triple integral.

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

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Q: 2 (2y² + 5xy 4 Ο α. χ' (y² + 2xy = y + 2) = C O b. x4 (y² O 2y + 4) dx + x (2x + 2y − 1) dy = 0 - -…

A: The given differential equation is; 2(2y2+5xy-2y+4)dx+x(2x+2y-1)dy=0.

Q: Let the position function of a particle be r = <t, t2,0〉. Find the tangential component of the…

A: Let the position function of a particle be r=t, t2, 0.To find the tangential component of the…

Q: 4. Which of the following functions grows at the same rate as ex as x goes to infinity? ex+3 e3x e2x…

A: We find which of the following functions grow at the same rate as ex as x goes to infinity: (1) ex+3…

Q: Find the cross product u x 7 where u = 2i -3j +k and = (7, - 3, 4). ü xü= Check Answer

A: We have u→=2i-3j+kor u→=2, -3, 1Alsov→=7, -3, 4

Q: Use Taylor series you already know to find the Taylor series generated by f(x) = x sin(6x) at x = 0

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Q: State whether the given sums are equal or unequal. 20 20 Aj and ke j=1 k=1 O Unequal O Equal > Next…

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Q: 2. d. lim f(x) = e. x-0+ f lim_f(x) = lim f(x) =

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Q: sinh³ (x) cosh (x) dx =

A: we have to evaluate the integral ∫sinh3x cosh8xdx use the formulas,…

Q: (a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) = PY PW POY

A: A particle moves according to the position function st=e4tsin5t To find the velocity and…

Q: 7. Find: y = In dx √6x-5 [ Lex (x+1)³.

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Q: a. Find the linear approximating polynomial for the following function centered at the given point…

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Q: 5 ΣΕ j=1

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Q: What is correct form of the particular solution associated with the differential equationy'''=8?

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Q: Question 3 Evaluate the limit. Hint: Factor and enter decimal answer. x + 3 x-3 x² + 8x + 15 lim

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Q: A piece of cardboard measuring 8 inches by 10 inches is formed into an open-top box by cutting…

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