Find the equation of the tangent plane to the surface determined by x³y² + z-30 = 0 at x = 3, y = 5. 2=

Q: If f(x) is a linear function, f(-2) = 4, and f(3) = 2, find an equation for f(x) f(x) =

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Q: A formula for the derivative of a function f is given. How many critical numbers does f have? f'(x)…

A: The critical number refers to the value at which the first derivative f' (x) of the real valued…

Q: cb+2π f" sin z dz = Sov20 a+2π a sin x dx

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Q: Does the set of all positive rationals form a group with the multiplication operation? Either verify…

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: An island is located 42 miles N26°10W of a city. A freighter in distress radios its position as…

A: The figure

Q: Solve dy/dx = y2 - 4

A: Given the differential equations we have to find solve the equation

Q: Find dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given value of the…

A: The given parametric equations

Q: Express each function as a composition of two functions. (Find f(x) and g(x) such that the given…

A: We have to find the given function as a composition of two functions f and g.

Q: Let f(x) = 3x + 3 and g(x) = −3x - 7. Compute the following. (a) (fog)(x) (b) (fog)(8) (c) (gof)(x)…

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Q: Evaluate the following limit. lim 8+←8 15 ln x X = Note: Input DNE, infinity, and -infinity for does…

A: Given,

Q: The table below gives the velocity of a runner at half- second intervals during the first three…

A: Given the table below gives the velocity of a runner at half-second intervals during the first three…

Q: (a) Find parametric equations for the line segment that joins the point P(2, 3, -3) to the point…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 12 + 2x -…

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Q: The temperature at a point (x, y) is 7(x, y), measured in degrees Celsius. A bug crawls so that its…

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Q: 1. Using the fundamental theorem of calculus part 1, along with properties of the definite integral…

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Q: What is a function that could have 17 X Question Help: Message instructor Submit Question Jump to…

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Q: Evaluate the following integral using integration by parts. √x20 In x dx

A: I=∫x20ln⁡xdx

Q: 5. Find the outward flux of the field F = xzi+yzj+k across the surface of the portion of the sphere…

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Q: For which value of t does the line given by the parametric equations x = t - 1, y = 1+ 2t, z = 3-t…

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Q: Determine the inverse Laplace transform: F(s) = (5 - 2s)/(s2 + 7s + 10)

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Q: An air traffic controller spots two airplanes at the same altitude converging to a point as they fly…

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Q: Profit The profit P (in dollars) made by a cinema from selling & Bags of popc x² 28,000 3,300, 0≤x≤…

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Q: A window has the shape of a parabola above and a circular arc below. Find the area of the window.…

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Q: Evaluate the following integral. 36 2 x - 36 36 x²-36 2 dx= dx

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Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

A: Order is the highest power of the derivative Degree is the power on the highest power of the…

Q: Find the area of the region enclosed by y=4.75x and x = 9 - y². 2 on 5 6 7 00 a Use horizontal…

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Q: 2. Find the derivative: a. y=ln(e^x)/(1+e^x)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the points on the curve where the tangent is horizontal or vertical. You may want to use a…

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Q: Find the differ y = √3 dy= = Evaluate dy fc x = 1, G y =

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Q: The vectors (8,-12, 16) and (8, 12, 5) are orthogonal. Select one: True O False

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Q: Solve 2(cos2x)y' + ysin(2x) = 4cos4x 0 =< x < pi/2

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 2xe…

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Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 5x² + y² = 4. maximum value:…

A: To find the maximum and minimum values of f(x,y)=xy on the ellipse 5x^2+y^2=4, you can use the…

Q: The equation r³+ y³ = 3ry defines a curve named as the Folium of Descartes. (a) Use implicit…

A: The equation  defines a curve named as the Folium of Descartes.By using implicit differentiation to…

Q: Find the domain of the function. h(u, v) = √3-u² - v² Ou+v≤3 Ou² + v² 0 Ou+v<3

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Q: For the following integral, (a) sketch the corresponding area, (b) approximate the area using the…

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Q: If 1800 square centimeters of material is available to make a box with a square base and an open…

A: Let the side of the square base = x cmLet height of box = y cm

Q: 5 4 --3- 2 -1

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Q: A large tank is partially filled with 150 gallons of pure water. Brine containing 2 pounds of salt…

A: Let A(t) be the amount of salt at any time t According to Question Rate of pumping in  gal/minRate…

Q: At what point(s) on the curve x = 6t² + 9, y = t³ - 5 does the tangent line have slope 2 (x, y) =

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Q: The following data show the number of months patients typically wait on a transplant list before…

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4 + x² -…

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Q: The magnitude of the vector (5,-2, 3) is √/38. Select one: O True O False

A: Given vector is: Let vector

Q: Find the differential of the function. dy = y = √ 8-t6

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Q: Evaluate the following integral, (9x - y²)dx + xy dy where C is given by x X = 5t, y = √t, 0 ≤ t s…

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Q: X 3. Verify that f(x)=- satisfies the conditions of the Mean Value Theorem on the closed interval…

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Q: -3 3 -3 I У X

A: From the given graph The horizontal asymptote is The vertical asymptotes are and

Q: Consider the following. {-x³ +3, -x² + 4x, x≤0 x > 0 Find the critical numbers. (Hint: Check for…

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Q: C T 3 2 1 To find the blue shaded area above, we would calculate: b So f(x) dx Where: 1 2 3 4 f(x) =…

A: We have to use the graph to find the integral substitutes and area  under the graph