Use Lagrange multipliers to find a vector in 3-space whose length is 4 V3 and whose components have the largest possible sum. (x, y, z) = ( %3D i

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

A: We will use the given formula of volume to find the volume of the tetrahedron.

Q: Express the given parametric equations of a line using bracket notation and also using i, j, k…

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Q: (y-3)/(x³+1) dy = y4dx is a separable differential equation. Select one: O True O False

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Q: a) Write the first three non-zero terms of the Maclaurin series for arctan(x). +... b) State the…

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Q: Find the intervals on which fis increasing and the intervals on which it is decreasing. f(x) =…

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Q: An open top box with a square base is designed to contain 2000 cm³ of volume. If we let z denote the…

A: An open top box with a square base is designed to contain 2000 cm3 of volume. If we let x denote the…

Q: Let u - (1, 2, 3), v (4, 4, -2), and w = (3, 0, -3). Find 4u + Sv - w. STEP 1: Multiply each vector…

A: The solution is given below

Q: 2- consider the set of all finite subsets of N, is this set countable or not, prove it?

A: Consider the set of all finite subsets of N, is this set countable or not, to prove it.

Q: х(4+sin 6x) 3. lim X→+0 х+1

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Q: Express the limit as a definite integral on the given interval. lim > x; In(2 + x;2) Ax, [2, 5] n-…

A: The solution is given below

Q: Find two unit vectors in 2-space that make an angle of 45° with 9i+ 4j. NOTE: Enter the exact…

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Q: 1 n + 1 n = 4 /- 8.

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Q: Direction: Determine the Inverse Laplace Transform of the functions using the Laplace of Integrals…

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Q: Find the ff: a. if the differential equation in question is variable-separable b. the given…

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Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: 2(2x? + у?)dx — ху dy %3D 0

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Q: Determine £(F}. F). 21 4s-18s +6 F(s) = %3D s(s-5)(s-6)

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Q: Approximate the area of the region bounded by the graph of f(x)=16-x and the a-axis on the interval…

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Q: xvx – 1 dx. | 1

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Q: 10. | xSin4xCos4xdx

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Q: АCTIVITY GIVEN : 2x 2x 1 2х + 3 1 f (x) = 1 –x 8 g(x) = 3(x + + 4 h(x) = 6 a.lim -4 · f (x) d.lim (8…

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Q: Use the graph of the polynomial function f(x) (a) to solve f(x) = 0, and (b) find the factorization…

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Q: Test your understanding. Write TRUE on the space provided if the statement is correct and FALSE if…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: For a general graph of a function x = g(y) that may go to the left and the right of the y-axis,…

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Q: The sum of two numbers is 12. if one number is x, what is the value of x such that the product of…

A: Here, let the two numbers be: x & y Then, x+y=12⇒y=12-x Now, the product of the two numbers be:…

Q: Set up a double integral in rectangular coordinates for calculating the volume of the solid under…

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Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. 4X-1 e lim…

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Q: Find the area of the region bounded by the following curves. y  =  x2 + 4x,     y  =  160 − x2

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. |2x - 9| dx

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Q: Instructions: (1) Use Limit Laws to find the limit of each given problem. (II) You may only use…

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Q: 2. The graph of y = cosh a is (a) concave up on its entire domain because y" = coshr > 0 for all r €…

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Q: Let g(x) = So" f(t) dt, where f is the function whose graph is shown below. (a) Evaluate g(x) for x…

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Q: S sin x In(cos x) dx

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Q: 0. 21XVX2 + 1 dx = 142 7, what is | 21uVu? + 1 du? Given that %3D 1

A: here just we put x =u so deside the function is odd or even so lets put u = -u 21(-u)(-u)2+1…

Q: At each point (x,y) on the curve, the slope is 2x+1. The curve passes through the point (-3,0). Find…

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Q: ance between the skew y = 5+ 2t, z = 5 – 4 y = 6, z = 1+3 e exact answer.

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Q: A stone is dropped from the upper observation deck of a tower, 100 m above the ground. (Assume g =…

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Q: Discuss the continuity of the function on the closed interval. Function Interval 9 - X, f(x) = [-3,…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: n²+1 Consider the sequence {a} '1=n'מ where a n²+4 • a. What is lim a ? n- 00 • b. What can you…

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Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 7 tan-1 Р(-8, 8); а —…

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Q: Suppose the graph y = f(x) lies entirely above the r-axis. Which of the following gives the %3D…

A: Let's find.

Q: 8. Differentiate each function. Express your answer in a simplified factored form. a. f(x) = (x +…

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Q: s (e² + 4 cos 8z dz 1+sin 8z,

A: A detailed solution is given below

Q: The sum of 2 numbers is 15. Find these numbers if their product is a maximum

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Q: dx 24. Integrate: J Ve-2x-1 А. Sec 1ex + C В. Sec-1e С. -Sec 1e* +с + C D. –Sec-le-* + C dx 25.…

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Q: Direction: Determine the Inverse Laplace Transform of the functions using the Laplace of Integrals…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: We need to find directional derivative.

Q: Eind the area of the given region. Use a graphing utility to verify your result. (Round your answer…

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Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y +…

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