1 (x-3)² y² + 289 64 Center: Vertices: Foci: Directrices: 1 Co-Vertices:

Q: Find an equation of the tangent line to the given curve at the specified point. x² - 1 x²+x+1 (1, 0)…

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Q: Problems: 1. Find the derivative of each function. Show your work by splitting the function into…

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Q: 1. Solve the homogeneous differential equation with the given initial conditions. y" + 5y + 6y=0…

A: If the two real roots of an auxiliary equation of a second-order homogeneous differential equation…

Q: Suppose that a population of bacteria triples every hour and starts with 600 bacteria. Find an…

A: Bacteria triples every hour. The number of bacteria increases 3 times in 1 hour3x3=32 times in 2…

Q: Estimate the indicated derivative by any method. (Round your answer to three decimal places.) y =…

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Q: The table shows the percent of workers that stayed in their chosen field. The data are modeled by…

A: Given: The data are modeled by the following quadratic function, where  corresponds to 1990 and  is…

Q: specified step size to estimate the value of the solution at the given point x* Find the value of…

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Q: Solve the given differential equation by undetermined coefficients. y" + 5y' + 4y = 12 y(x) =

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Q: O Find the to Nowings trignometric integrations dx (sin23 Scos x S

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

Q: Use the Maclaurin series sin x = S sint t Find the first three terms of the Maclaurin series of dt =…

A: The solution is shown in step-2

Q: Determine all the points where the given function is continuous 4 f(x,y)=√. y²+z²-4 a. x² + y² +2²4…

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Q: 2- Find the following limits: c) lim x ln (x) x→0+

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Q: Solve the given initial-value problem. y(x) = y" + 4y' + 5y = 35e-4x, y(0) = -6, y'(0) = 1

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Q: On what interval does the initial value provlem ty' = 3tsin(t) − y, y(1) = 2 have a unique solution.…

A: To determine the interval on which the initial value problem has a unique solution, we can use the…

Q: Use differentials to approximate the quantity. √8.7

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

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Q: Sandra is a 25-year-old woman who weighs 120 lb. She burns 300 - 50t cal/hr while walking on her…

A: Given calories burn (300-50t) calories per hr.Calories intake 80t in t hr.

Q: Find the critical points of f. Assume a is a constant. 1 13 12 = -√3x¹3 - a¹²x 13 f(x):

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Q: √h+6-h 5) lim h-5h³-3h²

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Q: Find all values x = a where the function is discontinuous. 6. f(x) = -3/(6x - 8)(8 - 2x)

A: A function is said to be discontinuous at a point where it is not defined.

Q: The graph of the function y = A. increasing and concave up on what interval? 3x³ + 9x² - 72x - 160…

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Q: The graph of a function is given. The x y-coordinate plane is given. The curve enters the window in…

A: To determine the intervals where f is increasingThe function is increasing when function goes up…

Q: 17 A company's marginal cost function is c(x)=- √x Find the total cost of the first 49 units (from…

A: Given marginal cost is we have to find the total cost of the first  49 units.

Q: Use the Chain Rule to find az/as and əz/at. z =tan(u/v), u = 3s + 7t, v = 7s - 3t

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Q: Write a double integral that represents the surface area of z = f(x, y) that lies above the region…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Here .We have to find the directional derivative .

Q: Use the given table to approximate f '(a) as accurately as you can. f '(13) = x 12.0 12.99 13 13.1…

A: Solution is given below in step 2.

Q: (Secx ) 4 (tan x)² dx.

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Q: Use the given graph to evaluate the following expressions. (a) (f+g)(2) (b) (f-g)(1) (c) (fg)(0)…

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Q: Use series to evaluate lim X x-0 (D x 1 et - 2x x - sin x

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Q: Consider the following function and express the relationship between a small change in x and the…

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Q: A population of viruses is increasing at a constant relative growth rate in the bloodstream of its…

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Q: A piece of cardboard measuring 14 inches by 9 inches is formed into an open-top box by cutting…

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Q: Write the equation for this graph in factored form and general form. (Remember to check your…

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Q: Solve the problem. Round your answer, if appropriate. 20. A ladder is slipping down a vertical wall.…

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Q: Find the exact length of the curve described by the parametric equations. x = 8 + 3t^2, y = 9 +…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

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Q: For each value below, enter the number correct to four decimal places. Suppose an arrow is shot…

A: Height To findaverage velocity

Q: 28. Differentiate a) f(x) = and SIMPLIFY the following functions: e-3x² cos² (4x-5) b) f(x)= (x-6)¹…

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Q: If 1400 square centimeters of material is available to make a box with a square base and an open…

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Q: Find the critical points of the functions f (x, y) = x² + 2y² - 4y + 6x, g(x, y) = x² – 10xy + y Use…

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Q: 4. Given the function f and point P, find a unit vector in the direction in which f increases most…

A: The solution is shown in step-2

Q: Find the center-radius form of the equation of the circle described and graph it. center (0,2),…

A: Explanation of the answer is as follows

Q: Find a polynomial function f(x) of least degree having only real coefficients and zeros as given.…

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Q: a. Write the equation of the line that represents the linear approximation to the following function…

A: The linear approximation of a function  at  is .

Q: Use Euler's method with step size 0.1 to estimate y(0.3) if y' = 5 – 3√√y, y(0) = 2.

A: Given

Q: Explain how the graph of Y = COS X can help you sketch the graph of y = sec x in the interval 0 ≤ x…

A: The solution is shown in step-2

Q: Find the maximum and minimum values of the function f(x, y, z)=x+2y subject to the constraints y²…

A: The solution is shown in step-2

Q: Pictured below are a contour map of f and a curve with equation g(x, y) = 8. Estimate the maximum…

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