Assuming 6x³ - 2y² + 4xy = 0 defines y as a differentiable function of x, use the theorem dy = dx dy dx |(1,-1) (Type an integer or a simplified fraction.) to find dy dx at the point (1,-1) E

Q: The Ninth Gate You arrive at the final gate, which leads into a building-like structure. You hope…

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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: Find the volume of a pyramid with height 29 and rectangular base with dimensions 3 and 8 using…

A: Let h be the height of the pyramid, and l and w be the length and width of the pyramid. Note that,…

Q: Consider the function f(x) = 12x³ +30x¹ - 160x³ +4. f(x) has inflection points at (reading from left…

A: Application of Derivative

Q: Use the washer method to determine the volume of the solid formed when the region bounded by y = x²,…

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Q: Use a differential to approximate. (Give your answer correct to 4 decimal places.) 4(3.98) (3.98)² +…

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Q: Find the distance from the point (4,-4,-5) to the line a(t) = (3, 1, − 4)t + (9,- 5,3)

A: Given equation of line:- a→t=3,1,-4t+9,-5,3

Q: Find the extreme values of f(x,y) = 4x + 6y subject to the constraint x² + y² = 13. 2 OA. The…

A: Question Find the extreme values of f(x,y) = 4x+6y subject to the constraint x2+y2=13

Q: Find the derivative of the function. y = In(3x²-x) + 4x

A: y=ln3x2-x+4xd dx(lnx)=1xd dx(xn)=nxn-1

Q: Find an equation of the tangent line to the curve at the point (1, -1-). y = x³e-x y =

A: To Find: Tangent line to y=x3e-x, at point 1, 1e

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

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Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.…

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Q: Use logarithmic differentiation to find the derivative of the function. y'(x) = X-3 x + 3

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Q: 2√3/3 3/2 21 7(²-1) ³92 - -dr = r (Type an exact answer in terms of .)

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Q: Express the given integrand as a sum of partial fractions, then evaluate the integrals. 1 1 y+2 2…

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Q: Find the volume of the solid generated by revolving the shaded region about the x-axis. 6 X₁ = 1, X₂…

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Q: Determine the average rate of change of the function over the domain graphed. (-3,5). y (3,5) 41 2…

A: From the given graph  of the function f(x)   The function is defined for the interval [-3,3]   To…

Q: 3. Find the centroid (, y) of the region bounded by y = 2 cos(3x) and y = 2 sin(3x) from z = 0 to z…

A: Centroid is given by x¯=1A∫abxf1(x)-f2(x)dx and y¯=1A∫ab12f1(x)2-f2(x)2dx where A=∫abf1(x)-f2(x)dx

Q: Find any relative extrema of the function. List each extremum along with the x-value at which it…

A: We have to find the monotone intervals and relative extremas.

Q: Use the theorem given below to find the curvature of r(t) = √62²i + 2tj + 2t³ k. k(t) = Theorem: The…

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

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

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Q: = Evaluate d5 dx5 [x³ − 3x + 1]. (a) (3x² - 3)5 (b) 0 (c) 72 (d) 6

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Q: K For the following demand function, find a. E, and b. the values of q (if any) at which total…

A: Given p = 700e-0.2q

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

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Q: h(x)=5.5x-3.42

A: We have given a polynomial  hx=5.5x-3.42 Leading term =5.5x

Q: . In the Gizmo, select sine wave so the parent function is f(x) = sin (x). A. The sine wave is a…

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Q: Q9 Given g(2) = 3 and g'(2) = 5. Evaluate f'(2) where f(x) = 5g(x) (a) 15 (b) 0 (c) 25 (d) 10

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Q: Q.#9 For above function, please find and classify any other removable or non-removable…

A: Q.9   For above function, please find and classify any other removable or non-removable…

Q: A vector with magnitude 4 points in a direction 340 degrees counterclockwise from the positive x…

A: let vector =V given  magnitude=V=4and direction=θ=340°now Vector V=<x,y>=?…

Q: ts) Let f(x) = 1. f'(x)= 2. f'(4)= 5x² tan(r) sec(x) Find the following:

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Q: Find √ √1 + x²dx

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Q: Consider the function f(x) Enter an antiderivative of f(x). Do not enter +c as part of your answer.…

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Q: 53 2 5 -4 -3 -2 -1 U V 2 3 Q Find the components of the addition of the two vectors u and v shown.

A: Ans= <0,-6>  For detail...go through the solution...I have solved step by step with the help…

Q: The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to…

A: Given:  fx=2-62x To Find:  To determine the domain of the derivative of fx and  then to evaluate it…

Q: Given the geometric sequence: 19, Find an explicit formula for an. an Find a7 = 190 3 1900 9

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Q: 4. Consider the graph to the right, containing the points (0, 1) and (1, 5). A. What function is…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: Find the 0 ≤ x ≤ 4 arclength of y = 4x²2 on

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Q: A volume is described as follows: 1. the base is the region bounded by y = e³.5x, y = 3.5x² + 0.9…

A: Given,             A volume is described as follows:             1. the base is the region bounded…

Q: A tank contains 500 gallons of salt-free water. A brine containing 0.25 lb of salt per gallon runs…

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Q: Assume that x=​x(t) and y​=y(t). Find dx/dt, using the following information. x^2+y^2=0.73: dy/dx=-2…

A: x2+y2=0.73given dydt=-2x=-0.3y=0.8d dx(xn)=nxn-1

Q: mine the average rate of change of f(x) = x³. - x over the interval 1 ≤x≤ 3.

A: We will find the required.

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

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Q: Let f(x)= = 4x² tan(x) sec(x) 1. f'(x)= 8x*sinx+4x^2*cosx 2. f'(1)= . Find the following:

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Q: [4-R] [CLO 15] Let f : R → Rx ↦ x2. That is,  is defined by the formula f (x) =x2. Give a formula…

A: The given function is: fx=x2

Q: The Map As you walk through Gate 4, you realize that Gate 5 is nowhere to be found. In front of you…

A: Given f( x ) is continuous in the given domain If a function is continuois at x = a then limx→a-f( x…

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

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Q: Suppose that f (x, y) = x³y². The directional derivative of f (x, y) in the directional (-3, 3) and…

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Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 4 meters per minute…

A: Need to find out the rate of changing of area outside the circle but inside the square changing.