Find the gradient of the function at the given point. Function Point f(x, y) = x² + 2xy (4,0) Vf(4, 0) = 8,8 > Find the maximum value of the directional derivative at the given point. 128

Q: Evaluate the integral using only methods taught in class, and simplify your answer. Do not ski…

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Q: valuate the integral using the Trigonometric Substitution metho x² (81-x²)3/²2 dx

A: Topic:- application of integration

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 6t5 L{f(t)} Submit…

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Q: 2. Let f(x) = f*cos² tdt. Find f(x) b. Find f'(x)

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Q: f(x) dx - f g(x)dx - f¹ g(x)dx A. -1 B. 7 C. 1 D. -7

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Q: Use integration by parts to solve. Simplify final answer and write in factored form. 2 (x)ln(cos(x))…

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Q: 13 If sec (0) = 3,0 ≤ 0 ≤, then 5 sin(0) equals cos(0) equals tan(0) equals

A: This is a basic trigonometric ratios problem

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Q: The bass population of a mountain lake was measured a year ago, and the lake was found to host 6,000…

A: This is a logarithmic problem

Q: 7. Compute the gradient of the following function f(x, y, z)= e-2z sin(2y) cos(2y);

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Q: Use the Midpoint Rule to approximate the integral. Then evaluate the actual integral. Round using…

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Q: Determine whether f(x) is differentiable at x = 0. Show your work. sin(x) cos(x)-1 3x + 1 f(x): = if…

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Q: Two cars are moving towards an intersection. One car is 160 meters north of the intersection and…

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Q: Integrate using appropriate U-Substitution. You must label u and du: (x - 1)(x + 1) 15x -5x³ S dx u…

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Q: Using geometry only, find the area under the curve. Include a sketch of graph for each region. Give…

A: Given fx=∫0636-x2+9 dx

Q: 1. (1-x) = y². ANS. y ln c(1

A: Given.

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, at the point (-1,л,0).…

A: Given :x=sin3ty=2tz=cos3tpoint -1, π, 0

Q: For f(x) = (a) fog 9 x-7 and g(x)= (b) gof find the following composite functions and state the…

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Q: Consider the following. (The graph is called a Witch of Agnesi.) y -2 Find the derivative of the…

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Q: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6) O…

A: To find the curl for the vector field  at the given point.Fx, y, z=6xyzi+6yj+6zkPoint=6, 7, 6

Q: 18. The volume of the solid that lies between the paraboloid z = 2x² + 2y² and the plane z = 6

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Q: (1) Theorem: The area A of the region bounded by the curves y = f(x), y = g(x), and the lines x = a,…

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Q: Find the percentage rate of change of f at the given value of x. 3/2 1(x) = (1 + ² + 3 + 2 + 3x + 14…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: 20. Which of the following is always true about the graph of f(x) on (-1,2)? (A) f(x) has an…

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: 44. y' - 2y = 0

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Q: 1. Find the projection of = 61 +3j + 2k onto = i-2j-2k.

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Q: O O Use the substitution formula to evaluate the integral. 1 6r dr 0√16+3r² OA. 19-4 √19 2 O B. -2…

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Q: 1). Find the first six terms of the sequence, starting with n = 1. an = 6 + (−1)n for n ≥ 1 a1=…

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Q: 40+ toz

A: Topic:- application of derivatives

Q: 23. Find the radius of the circle inscribed in a triangle formed by the lines 7x+24y-70-0,…

A: The given equations of the lines are: 7x+24y-70=0  ..........(1)21x-20y-70=0…

Q: Use a triple integral to find the volume of the given solid. boilisoqa oda buat amoldong guiwa (89)…

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Q: 5)  Solve the initial-value problem by using integrating factors. xy' = y − 3x3, y(1) = 0 y(x) =

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Q: 16. I. g has a jump essential discontinuity at z = 1. II. g has an infinite essential discontinuity…

A: We need to determine discontinuity.

Q: Evaluate ff sin(9x² + 4y²) da, over the region in the first quadrant by the ellipse 9x² + 4y² = 1.

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Q: 4. 5. 6. I. lim f(x) does not exist. 2-3 II. f has a removable discontinuity at x = -3. I. f has a…

A: We need to determine discontinuity.

Q: 8. THE ANSWER PROVIDED IS DOESN'T MAKE SENSE. HOW DOES 21+7 = 38? PLEASE PROVIDE CORRECT ANSWER…

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Q: Find the second derivative of the function. f(x) = sec x

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Q: Analyze the following equation and graph it. 36 9-8 sin 9 r= Identify the conic that the polar…

A: Solution is given below:

Q: A force of 960 newtons stretches a spring 4 meters. A mass of 60 kilograms is attached to the end of…

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Q: Use cylindrical coordinates to find the volume of the solid bounded above by z = 3x and below by z =…

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Q: Find the average rate of change of the function over the given interval. f(t) = 6t² - 5, [1, 1.1]…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. [(5y +…

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Q: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts,…

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Q: 4

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Q: 8. Evaluate the line integral fx'dx + xe 'dy where C is the closed path along the triangle in the…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: A population of 440 bacteria is introduced into a culture and grows In number according to the…

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Q: Write the sum as a product: sin(16.76) + sin(12.96) = > Next Question

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