Find the area of the triangle with vertices P(1, 3, –6), Q(0,0, 0) and R(4, 5, 1). NOTE: Enter the exact answer. A =

Q: A Use the method of Lagrange multipliers in Problems 7-10. I SL.

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Q: Find Duf at P. f(x, y, z) = 4x'y'z"; P(1, –2, 1); u = + %3D Duf i -Tem

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Q: Determine whether the alternating series converges. 3ln k E(- 1)*: k k=3 The series diverges. The…

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Q: p³ + x² – 4 4x = x +1+ - 1. Consider the function f(x) Note that - 4° x² – 4 x2 (x2 – 12) (т? — 4)2…

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Q: Set up and evaluate the integral for finding the area and moments about the x- and y-axes for the…

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Q: Evaluate the integral of: * dx x2 – 2x + 50 arctan (x - 1) + C arcsec (x - 1)/7 + C O 7 arcsin (x -…

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Q: Find the directiunal deavative of the function at the given pornt in the direction Lof the rectorv…

A: Given problem:- Find the directional derivative of the function at the given point in the direction…

Q: Consider the function f(x, y) = 2x² – 7y² subject to the condition x? + y = 25. Use Lagrange…

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

A: To Find : a) A vector oppositely directed to v=17,-8 and hal the length of vb) A Vector that as…

Q: Evaluate the integral. S(-241 - s)at 3 xdx = 2 15 given, a'dr = x²dx = dx = 1, O -36 O -146 O -114 0…

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Q: A factory selling cell phones has a marginal cost function C'(x)=0.01x^2-3x+229 where x represents…

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Q: Find an equation of the plane pirpendicular to the line through (2,2,-4) and (9, "1, 3) and…

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Q: Find the gradient of the function at the given point. g(x, y) = 18xe/x, (10, 0) Vg(10, 0) =

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Q: x³ + x? – 4 1. Consider the function f(x) 4.x = x +1+ x2 Note that 4 x² – 4 - x²(x² – 12) (x² – 4)²…

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Q: Determine whether the series converges using the limit comparison test. 4k2 – 2k +9 Σ 20k7 + k – 20…

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Q: Find the vector component of v = (4, – 1, 7) along b = (6, 6, –7) and the vector component of v…

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Q: The graph of f' (x) is given below. On what interval(s) is the value of f(x) increasing? Glve your…

A: Graph of the derivative function is given, we have to find the increasing interval of f(x)

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x - y + z…

A: To Find : Equation of plane passing through (-3,8,-8) that is perpendicular to the plane7x-y+z=2 and…

Q: Find the directional derivative of the function at P in the direction of v. h(x, у, 2) %3D хуz, P(4,…

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Q: 3. f(x) = A. x = 0 B. x = 1

A: We know that a function is continuous at x=a if limx→a-f(x)=limx→a+f(x) =f(a) The function f is…

Q: Consider integral 1 •1-z 1 II T (a, y, 2)dzdydz. nge the order of integration and rewrite the above…

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Q: 2y Find the directional derivative of f(x, y, z) at P(5, 2,-4) in the direction from P to Q(4, 3,…

A: To find the directional derivative of the given function.

Q: Solve for x in terms of a and b. log x = - 10(log a + log b) + 8 log b° + 5(log b – log a) = x Write…

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Q: Use the triple integral to find the volume of a solid G enclosed by surfaces x = y*2 and planes…

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Q: Find Duf at P. 2. f(x, y, z) = 4x³y°z²; P(1, –2, 1); u = i+ Duf = i

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Q: Find the vector component of v = 2i – j + 3k along b = 2i + 4j + 4k and the vector component of v…

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Q: Determine whether the series converges. Σ Vk+ 3 k=1 The series converges. The series diverges.

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Q: Let a = ci + jand b = 8i + 40j. Find c so that a and b are orthogonal. c = i

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Q: 4. Let f(x) be a function that satisfies f(3x) dx = 1 and 3f(x) dx = 15. Calculate f(x) dx. Show all…

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Q: Find the directional derivative of f at the point P in the direction of a. f (х, у) — 923 — 6у3;…

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Q: 1. State the domain and range of {(x, y)|y = + 3}.

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Q: y" + 4y' + 6y = 1 + e¬2t , y(0) = 0, y'(0) = 1

A: We need to solve the differential equation.

Q: Find the gradient of the function at the given point. In(x2 – y) – 9, (3, 8) z = Vz(3, 8) =

A: use partial derivative for finding the gradient.

Q: Find an equation of the plane that passes through the point P(-7,-2,5) and has the vector n = (-7,4,…

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Q: 33. f(x, y) = xr – 3xy² + 6y²

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Q: 3. Determine all the roots (real or complex) of the polynomial p(x) = 2x4+13x³+27x2+13x-15.

A: Since you have posted multiple questions. As per guidelines, we"ll solve only first question. If you…

Q: ES dx = 4x + C

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Q: Find the directional derivative of f(x, y, z) 2y at P(5, 2,-4) in the direction from P to Q(4, 3,…

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Q: Which method/s can be used to find the volume of solid of revolution of the following? (Choose from:…

A: Note: we have to solve only 1 question so here 1,2 are related so I solve 2 question. Also breif…

Q: True or False - In deriving the differentiation rules, the word proof is used instead of the word…

A: True, in deriving the differentiation  rules the word proof is used instead of the word derivation.…

Q: Test the series below for convergence using the Ratio Test. n+5 52n +4 The limit of the ratio test…

A: Given

Q: af when r = 2, t =- 1 of the function ar 4. Use the Chain Rule to find- f(x, y, z) = e3xy² cos 2xyz…

A: This is a problem related to chain rule for differentiation. Based on the formula we will find out…

Q: Compute the length of the curve r(t) = (-6t,4t + 4, –5t – 3) over the interval 0 < t < 7. (Use…

A: The curve rt=-6t, 4t+4,-5t-3 over the interval 0≤t≤7

Q: y' + y = sin x.

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

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Q: Find the directional derivative of f at the point P in the direction of a. i-j f (x, y) = 2x3 – 6y³;…

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Q: Find the speed over the path r(t) = (sin(3t), cos(6t), cos(3t)) at t = (Use symbolic notation and…

A: The path r(t)=sin(3t),cos(6t),cos(3t) at t=π2

Q: (3y²+ 2x³)dy + 2xydx=0

A: As we know that; The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. The solution…

Q: 2. Evaluate the following limits. cos X h. lim-

A: Limit