If z = x2- xy+ 3y2 and (x, y) changes from (3, -1) to (2.96, -0.95), compare the values of delta z and dz.

Q: The number of bacteria in a flask grows according to the differential equation dy/dt=0.09y In this…

A: The given data is: dydt=0.09y

Q: Let r(t) = (t², 1 — t, 4t). Calculate the derivative of r(t) · a(t) at t = 2, assuming that a(2) =…

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Q: 5. The Cobb-Douglas production function for a new product is given by P(x, y) = 10x406, where x is…

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Q: Use the graph M of the derivative of f to locate the critical points zo at which has neither a local…

A: see below the answer and explanation

Q: 1. Find the point (s) at which the following parametric curve x = t², = t³ - 9t intersects itself.…

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Q: Find the Inverse Laplace transform for the followi 2-5s (s-6) (s² +11) a) F(s) = =

A: Note:- Since you asked multiple equations ,according to our policy we can solve only first question…

Q: Show that the scalar field = 1/R], which is defined everywhere except at the origin, is a potential…

A: If f is a function then ∇f=fxi+fyj+fzk. f is a potential function of F if ∇f=F

Q: A company manufactures and sells x smartphones per week. The weekly price-demand and cost equations…

A: According to question,Given Functions,p = 500-0.5x,Cx = 20,000 + 135 x

Q: For each function, use our techniques to sketch the graph. Include asymptotes, at least one…

A: (a) Given that,              y=xx-1 x-intercept:            y=0 ⇒xx-1 = 0           ⇒x=0…

Q: -Calculate the minimum for the function f(x, y) = 2x² + 2x^² - xy

A: According to question,Given Function,fx,y = 2x4 + 2y4-xy

Q: Find the absolute extreme values for a(z) = 6 - 476 on [1,2].

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Q: 5. Find the maximum height above the x-axis of the polar curve r = 2+2 cos(0).

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Q: 10. Find the absolute maximum and the absolute minimum of f(x, y) = 2x² + y² + 2 over the disk D…

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Q: Consider the four graphs shown below. For each graph, select Yes if satisfies the following…

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Q: 11. Use matrix multiplication to show that two clockwise rotations of radians produces the same…

A: Let's denote the clockwise rotation matrix by R(theta), where theta is the angle of rotation in…

Q: Find the average height of the paraboloid z = x² + y² over the square 0≤x≤3, 0≤ y ≤3. The average…

A: Given data The equation of paraboloid is, z=x2+y2. The limits of the square is 0≤x≤3, 0≤y≤3.

Q: Find the critical points of the following function. f(x) = 9x 2 x² +81 Select the correct choice…

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Q: they​ occur, for the function f(x)=x2−18lnxon the domain [1,11].   Select the correct choice below​…

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Q: 1. Given that y² = 48sin 0 and dy/dt = -5, find de/dt when 0 = TT/6

A: Given y2 = 48sin(thita) dy/dt = -5 thita = pi/6

Q: Use implicit differentiation to find the following. (If only the x-coordinate is given, you must…

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Q: If f(x) = 3 x-3 7 and g(x) = 7x³ + 3, are f(x) and g(x) inverse functions?

A: The functions f and g are inverse functions for each other if and only if f∘gx=g∘fx=x

Q: 5. area A of the surface generated by rotating the region R about the line y = -3. Let R be the…

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Q: You are standing above the point (2, 2) on the surface z = 15 - (3x² + 2y²). (a) In which direction…

A: Please see the below picture for detailed solution.

Q: Determine whether the function f has a derivative at c. If it does, what is f'(c)? (If an answer…

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Q: Suppose that f(x) 13x - 3 In(x), x > 0. (If an answer does not exist, enter DNE.) (a) Find all…

A: Here we have to apply the application of differentiation.

Q: 10. Find the indefinite integral J dx (3+5)2 dx

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Q: pany makes computer chips from square waters of silicon. A process engineer wants to keep the side…

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Q: how do you determine it's a quarter circle?

A: Question is ∫-100100-x2dx is quarter circle

Q: 5. Consider the region R bounded by y=1-x² x = 0 and y = 0 [This region is used to answer questions…

A: Draw the graph and then select the region.Take a small volume of a cross section area and integrate…

Q: Evaluate the integral. [²7X 71 7x√√x² + 9 dx

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Q: dw Use the Chain Rule to find &#: w = xysinz; Dx = xet, yet, zzaresin 2

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Q: 7. The Von Bertalanffy differential equation has successfully modelled the growth of a human tumo…

A: Given that expression dVdt=aV23-bVWe have to show that above differentital equation has solution…

Q: -2y time does y increase to 100 or drop to 1? Round your answer to four decimal places.

A: we will find the required.

Q: If = {(x, y) | x² + y² ≤ 4, x>0} then: 16₂ (3x + 5y) dA= Question Help: Video

A: Here we have to find the double integral.

Q: Find the volume of the solid enclosed by the paraboloids z = 16(x2 + y2) and z = 2 - 16(x2 + y2)

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Q: 6x-7 The total cost (in hundreds of dollars) to produce x units of perfume is C(x)= 5x+1 (a) Find…

A: C(x)=6x-75x+1(a) aversge cost(C¯(x))=C(x)x

Q: The first five terms of the sequence tn = 6(-1)n-1 are....

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Q: Consider the curves y = x^2 sinx and y = -1 - sqrt(1 + 4(x + 2)^2 ).    Find the x-coordinates of…

A: To find the x-coordinates of the points of intersection of the two curves, we need to solve the…

Q: Evaluate the integral. 9 y4 SS 4 y 3 y X dxdy

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Q: B: Find the Inverse Laplace transform for the following functions: 2-5s (s-6) (s² +11) a) F(s) = (b)…

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Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 7…

A: As we know that x = rcosθy = rsinθ

Q: Solve the given differential equation. √√x² + y² dx - 4ydy = 4xdx Choose the correct answer below.…

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Q: Use the Laplace transform to solve the given integral equation. + 6 ² ₁² - f(t) + f(t) = cos(t) (t =…

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Q: On which interval f(x) = -2³ + 3x² - 4 is concave upward? O a. (-1,1) O b. 1 Od. >1

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Q: Determine whether the series is convergent or divergent by expressing the nth partial sum s as a…

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Q: If f'(x) 0 for all x, which of the following could be a table of values for f? x -1 0 1 (A) f(x) 6…

A: If function f is decreasing then f’(x) <0. Use this concept.

Q: : )₂² dx = 2M²+1 Jam x m+1 +( Connected to AmerEast-1. [ 2/²3 - 42²2 + 92]," 니 | [213 - 4 ( 22² +9…

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Q: Find [[ cos (x² + y²) dA where D = {(x, y) | 9 ≤ x² + y² ≤ 25}

A: We need to evaluate :