Assuming that the equation below defines y as a differentiable function of x, find the value of dy/dx at the given point. 3x² + xy + 2y²-16=0, (2,1) dy dx (2,1) = (Type an integer or a simplified fraction.)

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Q: Find the derivate of the functions: a) F(x) = -3x²=4 : f'(x) = b) g(v) = 3 g'(v) = 2√² +5V-9 c) f(x)…

A: We need to find out the derivatives of the given functions.

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A: Determine the X intercept of the plane [x, y, z]= [3, 1, 3]+ r[1, 1, -1]+ t[0, 1, 3]

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A: Solved below

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: Q8 Find the slope at x = 2 on the graph of f(x) (a) -3 N/W (b) 3/3 (c) 3 4 = 3 (d) 0

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Q: The postal service will accept a box for domestic shipment only if the sum of its length and girth…

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Q: Find parametric equations of the line that contains the point P(3, 1,-2) and intersects the line L:…

A: The solution is shown below-

Q: Consider the function f(x) = 2 +² + 3x at (0, 2) we have: -slope:5 - equation of the tangent line at…

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Q: Suppose the demand for a certain brand of a product is given by ​D(p)=−p^2 / 416+450​, where p is…

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Q: Find lim f(x) if, for all x > 1, x → 00 4 12ex - 24 4ex X 3√x √x-1

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Q: Ifis decreasing and its graph is concave pon (0, 1), which of the following could be graph of the…

A: If f is decreasing and its graph is concave up on (0, 1). Wich of the following is the graph of f'…

Q: A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material…

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Q: Consider the following problem: a farmer with 650 feet of fencing wants to enclose a rectangular…

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Q: Find the mass of the solid bounded by the planes x+z=1, x-z = -1, y = 0, and the surface y=√z. The…

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Q: -1 If ƒ(x) is a positive 1-1 function with inverse ƒ−¹(x) with f(a) = c and ƒ(b) = d then d π ñ ["°*…

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Q: Q11 Compute (a) [3.14] = dx (b) Compute [54] = d 5-4x- dx 3

A: To compute the following. (a) ddx3.14 (b) ddx5-4x3

Q: 2 Functions f and g are defined by f(x)=2(3+1)₁³ ,x+0 and 1 g(x)==-=-3₁ X≠3 respectively. (a) Find f…

A: The given functions are:f(x)=23+1x ;    x≠0       and        g(x)=1x-3 ;     x≠3

Q: The cost of producing x bags of dog food is given by C(x) = 900+√700 + 50x²-x where 0≤x≤ 5000. Find…

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Q: The sum of integrals below give the area of a region in the xy-plane. Sketch the region, label each…

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Q: The integral gives the area of the region in the xy-plane. Sketch the region, label each bounding…

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Q: Q15 Find all non-zero derivatives of the following function: f(x) = 5x³ - 7x² + 9x - 1

A: Here we differentiate f(x) with respect to x until it becomes a constant

Q: Answer the following questions. 1 A function f is given by f(x) = (x+1)|x+3| x+3 (a) Express f(x)…

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by…

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Q: A car rental agency has a budget of $3.2 million to purchase at most 120 new cars. The agency will…

A: We can solve it as given below

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e-5x (Use…

A: We draw the graph of the function and find the total area by integrating

Q: Find the centroid of the region cut from the first quadrant by the circle x² + y² = 81.

A: Find the centroid of the region cut from the first quadrant by the circle x2+y2=81.

Q: Let f(x) = 4x² - 2x4. Find the open intervals on which f is increasing (decreasing). Then determine…

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Q: Write the equation of the tangent line to the curve at the given point. x² + y² + 6x - 3y + 7 = 0 at…

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Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

A: Given: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then…

Q: Use the washer method to determine the volume of the solid formed when the region bounded by y =…

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Q: у-х-2 (1-1) х-у

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Q: Find the derivati: (2) g(x)= g'(x) = 25 35+2 (5) 3 2 b) f (x) if f(x) = 5x ² + 6x² - 9 f(s) (x) =

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Q: Evaluate the limit sin 2x 8x lim x→0

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Q: Draw an accurate diagram of what follows and find resulting distance to the port: A ship sails on a…

A: Please see the below picture for detailed solution.

Q: J xlnxdx X X

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Q: why was x tan(t)?

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Q: has a point of inflection. 2 z = 2 3. r = 0, 4 4. # = 0, -4 g 5. r = 0, 1. Find all values of at…

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Q: Sketch a graph that possesses the characteristics listed below. f is increasing and concave up on…

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Q: Using the equation y= x^3/ x^2 - 4 Determination of equations of horizontal asymptotes (if they…

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Q: Complete the parametric equations of the line through the points (1,8,3) and (4,-6, (t) = 1 + 3t…

A: The parametric equation for the line through (x, y, z) and (a, b, c) is: (x, y, z)+t((a, b, c)-(x,…

Q: Consider the curve r(t) = (6 cos(t), 6 sin(t), e), 0 ≤ t ≤ π. Find r'(t). r'(t) = Consider the plane…

A: Given curve:- rt=6cost,6sint,et

Q: 3) Find the general solution to y′ = sec^2 x.

A: To find general solution.

Q: For each cost function (given in dollars), find the cost, average cost, and marginal cost at a…

A: Given : a. at q = 1000 Average cost = 128000/1000 = 128 dollars / unit   Marginal cost for q=1000

Q: Find the extreme values of f on the region described by the inequality. (If an answer does not…

A: Given, f(x, y) = e-xyRegion, x2 + 4y2 ≤ 1   Finding the critical points, ∂f∂x = -ye-xy∂f∂x = 0, y =…

Q: Given the points A: (-6,-4,2) and B: (3,-2,0), find the vector u = AB

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Q: Let (5,2,2). P-(1.-2,0). A=(4,3,0) be points in R³. Find the general equation of the plane P in R³…

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Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

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