Compute the average rate of change of the function on the given interval. g(x) = x³ x on [4, 5] -

Q: A golf ball manufacturer knows the cost associated with various hourly production levels, given…

A: Production cost for golf balls is given as,

Q: (a) Find the unit tangent vector on the curve r(t) = [cos(t),2t, 3sin(4t)] when t = 0. (b) Evaluate…

A: Given curve:Unit tangent vector is given by,Therefore,

Q: If h (x) = (x² – 2x 43 04/0 0 - 12/25 3 00 - (x² – 2x − 1) ³, then h' (0) =? - 43

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Q: Find the absolute maximum and absolute minimum of the following function on the given interval. ƒ(x)…

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Q: (a) Find and sketch the domain of the function f(x,y)=√x+2+√√√y+3 (b) Evaluate the limit -8xy lim…

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Q: Use partial fraction decomposition to find the following integral -da 24-1

A: I=∫x2x4−1dx

Q: taman X Find dimensions of rectangular fenceline that uses the least amount of material and will…

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Q: An account earns an APR of 4.7% compounded as often as imaginable ("compounded continuously"). The…

A: The given rate is, r=4.7%=0.047 compounded continuously.For the continuous compound, the annual…

Q: A mutual fund is currently valued at $70 per share and its value per share is increasing at a rate…

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Q: For the vectors u = 3ỉ − 8j + 2k and - v = 4i - 2j – 4k we have - ü × v = 28i + 20j +38k. Select…

A: The given vectors

Q: A student solves an optimization problem as in Model 1, except that in the problem Mini and Max are…

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Q: HOMOGENEOUS DIFFERENTIAL EQUATION Solve the following differential equations using HOMOGENEOUS DE.…

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: lim √xe-x/2 x → 00

A: L=limx→∞xe−x/2

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

A: To find the parametric equations for the line segment that joins the point .Note: Since the student…

Q: Solve the given boundary-value problem. y-10y+25y=0, y(0)=1 y(1)=0

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Q: The indicated function y₁(x) is a solution of the associated homogeneous equation. Use the method of…

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Q: Consider the following differential equation to be solved by the method of unde y" + 2y = -18x²e2x…

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Q: Determine if the series diverges. If it does diverge, type a upper case D as your answer, and if the…

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Q: For each of the indefinite integrals below, choose which of the following substitutions would be…

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Q: List the first five terms of the sequence. a1 = 2, : 2, a n + 1 an + 1 = 2an + 4 21 2 а2 8 12 14 16…

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Q: Give the partial fraction decomposition for the following function. 2 x²-2x-8 2 2 x-2x-8 ||

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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 median home value in Texas and Missouri (adjusted for inflation) are shown below. Year Texas…

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Q: What is the unit tangent vector T(t) on the curve r(t) = (cos(t), 3t, 2 cos (2t)) when t = 0? Select…

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The given polar curve .The aim is to find the slope of the tangent line to the polar curve at the…

Q: Let 16x-5 1x² +5 Enter the exact value of the one-sided limit lim f(x) 3-2 f(x) = if x ≤ 2 if x > 2

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Q: (a) Find the unit tangent vector on the curve r(t) = [cos(t), -t, -4sin(3t)] when t = 0. (b)…

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Q: Sales The profit for a product is increasing at a rate of $5600 per week. The demand and cost…

A: The profit for a product is increasing at a rate of  per week.The demand and cost functions for the…

Q: The general solution of the equation y'' − 6y' + 9y = 0 is given by y(x) = e^(3x)(C1 + C2x). Is this…

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Q: Find the domain of the function f(x, y) = ln(x² + y² - 9) + √-y.

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Q: Find a Cartesian equation for the curve. r = 5 sec (0) 2π X

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Q: The diagram below shows upper and lower sums for the function f(x)=√√x+1 using 4 subintervals. Use…

A: given function

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

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: Consider the curve

Q: Suppose f(x, y) = x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: Find the maximum and minimum values of the function f(x, y) = 2x² + 3y² - 4x - 5 on the domain x2 +…

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Q: Use the Table of Integrals in the back of your textbook to evaluate the integral: -xs -X sec (3x) +C…

A: Given Indefinite integral as follows

Q: 6. Given f(x) = 3x - 1 A. Find (f-g)(x) B. Find (fog)(x) report domain and simplify C. Find (3) (2)…

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Q: Let h(x) = 6x² +1+17x Determine the critical values of h. If multiple such values exist, enter the…

A: Given, .For find critical valuer put h'(x)=0.

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

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Q: Use Rolle's Theorem and a proof by contradiction to show that the function f(x) = 6x³ + 4x - 11 does…

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Q: A boat is pulled by a winch on a dock, and the winch is 12 feet above the deck of the boat (see…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Assume that  are both  differentiable  functions of t.(a) To find , given that (b)  To find , given…

Q: 2. a. C. Determine the critical number(s) for the following functions. f(x) = 17-6x + 12x²…

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Q: What is the unit tangent vector T(t) on the curve r(t) = (sin(t), 3, 2 cos (2t)) when t = 0? Select…

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Q: Consider the function f(x, y) = x²y+y³ — 27y. f has f has a maximum a minimum f has a saddle f has…

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Q: Find the measures of the sides and angles. Round angle measures to the nearest tenth of a degree.…

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Q: Find f. f(t) f'(t) = t³ + -/-/7₁ t5 t> 0, f(1) = 4

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Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01 cm/min.…

A: Radius = 60cmdr/dt = 0.01 cm/min.