Differentiate the function. f(x) = 5x ln(2x) − 5x

Q: Write an equation for a rational function with: Vertical asymptotes of x = -3 and x = 1 x intercepts…

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Q: 4 2 1 L L 3 (x + y)² dy dx.

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Q: 2. g(x) = x³ + 5x²

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Q: 5. Simplify the expression in terms of i. Leave your answer in a radical if the radical cannot be…

A: To simplify the expression in terms of i. (i) -6-15 (ii) -637

Q: A water balloon is thrown upward from a window that is 75 meters high with an initial velocity of 19…

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Q: Find Vf at the given point. 3 2 f(x,y,z) = x² + y² - 2z² + z lnx, 222 (1,5,1)

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Q: Prove that the following function is harmonic and find its harmonic conjugate: 2e^x cos y

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Q: Identify the location and value of any relative maxima or minima of the function. Part: 0 / 2 Part 1…

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Q: You need to construct an open-top rectangular box with a square base that must hold a volume of…

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Q: Solve for difference quotient, and explain why you are doing each step. As if you are teaching this…

A: Question -   Solve for difference quotient,   F(x)=1/(5x-8)

Q: Find the exact value of each of the remaining trigonometric functions of 0. 24 25' sin 9= 90°…

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Q: at the point (π, -5T). The equation of this tangent line can be written in the form y = mx + b where…

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Q: Let f(x)=3x+2x^3 Find f^-1(22)

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Q: Find the zeros of the function and state the multiplicities. d (x) = 2x (2x+3) (4x+7)(x − √5) (x +…

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Q: How would I find the limit of the following quotient? sin(x^2 + y^2) / (x^2 + y^2) lim…

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Q: A company produces computers. The demand equation for this computer is given by p(q)=−5q+6500. If…

A: let revenue function = R( q ) as we know that R( q ) = q.p( q )

Q: Find the directional derivative of f(x, y) = exy in the direction u = (,) at (xo, yo): (0,1). 3545…

A: Given query is to find direction derivative.

Q: 16x²64x25y² + 150y - 161 = 400 a) General Equation form b) Standard Equation form c) Distance…

A: As per our guidelines we can answer only 3 subparts of the given question, so kindly repost the…

Q: Solve the following differential equations: dy dx b. (x³ + xy²) dy dx a. + 2y = e³x = 2y³

A: We have to solve the given differential equation.

Q: Let f(x,y)=x² - xy + y²-y. Find the directions u and the values of Df(1,-1) for which the following…

A: As you have asked for multiple subparts so I will answer first three subparts as per the guidelines.

Q: a) Solve the following; 0 < |2x - 71 ≤5

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Q: Find the length of the curve. r(t) = (st 3 co

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Q: . Find all points on the graph of the function f(x) = 2 sin x + sin²x at which the tangent line is…

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Q: 3x-5 Use the quotient rule to differentiate the function f(x) = 4x+3 f(z) =

A: Given query is to find the derivative.

Q: Write an equation for a rational function with: Vertical asymptotes of x = 6 and x = 7 x intercepts…

A: Given query is to find the function.

Q: Find f'(x). f'(x) = f(x): Find f'(-1). f'(-1) = 14 equation = -9x + 5 Find the slope and an equation…

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Q: Please use strong induction to prove that each integer n that is greater than 0 can be written as a…

A: INTRODUCTION Mathematical induction is a method used to prove statements about a set of positive…

Q: The endpoints of a diameter of a circle are shown. Find the center and radius of the circle. (-2,2)…

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Q: an equation of the line

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Q: Given Cost and Revenue functions C(q) = q³ - 10q² +56q+5000 and R(q) = -3q² +2400q, what is the…

A: Given  Cq=q3-10q2+56q+5000Rq=-3q2+2400q To find the marginal profit, Marginal Profit=Marginal…

Q: Determine the derivatives, dy dz dy a.y = logg (7) → b.y = ln (2³) c.y = In (7x) → d.y = log3 (2)→…

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Q: Write the given differential equation in the form L(y) = g(x), where L. is a linear differential…

A: The differential equation is given by 3y''-8y'-3y = 5 To Write: The differential equation in the…

Q: The table shows total earnings, y (in dollars ), of a food x,0,1,2,3,4,5,6 y,0,18,40,62,77,85,113 a.…

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Q: A = y=x² (-2, 4) -2 4 2 (1, 6) 3y=2x+16 (2, 4) y=8-2x 2

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Q: 16x²64x25y² + 150y - 161 = 400 a) Distance between the foci b) Center c) Equation of the transverse…

A: As per our guidelines we can answer only 3 subparts of the given question so kindly repost the…

Q: Find the absolute maximum and absolute minimum of the function z = f(x, y) = x² - 10xy +10y on the…

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Q: Current Attempt in Progress Use the root test to determine whether the series converges or diverges.…

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Q: te the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: Find the linearization L(x,y) of the function f(x,y) = e cos (9y) at the points (0,0) and 0,

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Q: 4) B 11 km 17 km 10 km с

A: Given:

Q: Solve the following quadratic equations: i. 8p²+72=0 16 ii. (a-3²=-¹6 iii. m(m+5)=24 (solve by…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Differentiate R = esin(58)

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Q: 4) Graph the following equation; Y= x²+2x+3

A: given :y=x2+2x+3

Q: Find the horizontal and vertical asymptotes of the curve. x² + 10 8x²-47x-6 y = Step 1 To find the…

A: Given that  y=x2+108x2-47x-6 Making numerator 0 we get 8x2-47x-6 =0 x=-(-47)±-472-4×8×-62×8,…

Q: S 1 √4x²+81 dz +C

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Q: Determine whether the series converges; if so, find its sum. If the series diverges, indicate that…

A: Given series is ∑k=1∞54k-45k

Q: f (x) = = 1 5x-8

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Q: 1)Find the center and radius of the circle: 2 2 x² + y² − 8x + 6y = 0

A: To find the center and radius of given circle.

Q: For a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B is…

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Q: If f(x) = 3 cos (4 ln(x)), find f'(x). Find f¹(3).

A: The function is given by fx = 3cos4lnx To determine: The expression of f'x and the value of f'3.