Find the length of the arc of the curve y = 2 34 3 (4 x − 1)2 from x = 0 to x = 6

Q: At which points on the curve y = 1 + 40x³ - 3x5 does the tangent line have the largest slope? (x, y)…

A: we need to find out the points on the given curve where the tangent line has largest slope.

Q: Evaluate the limit using L'Hospital's rule if necessary lim (1 + 4) * I→∞

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Q: Find the centroid of the triangular region cut from the third quadrant by the line x + y = -3.

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Q: Q. 3 Given z = x²y, x = 2t+s, and y = 1 - st². dz We have to find dt s=1, t=2. We first find dz dt

A: Given data÷ z=x2y ,x=2t+s, y=1-st2 dzdt at s=1,t=2 Here, z=fx,y and x=fs,tand y=fs,t

Q: Evaluate the limit using L'Hospital's rule if necessary x 5 7 lim (1+1)

A: To find the limit

Q: 2. Use the graph to determine: (a) Is the degree even or odd? (b) Is the leading coefficient…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = -5x² - 2xy-4y²…

A: To find all local maxima, local minima, and saddle points of the following function. fx,…

Q: B. Consider the following equation (x-3)² 5(x + 1)²(x-2) f(x)=₁ 1. The rational function above has a…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

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Q: Let f be the function defined by f(x) = x - 2 sin(x), 0≤x≤n. On which interval(s) is f increasing?…

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Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

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Q: Find the distance from the point (-6,3,1) to the plane: x-2y-4z = 8.

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Q: Find the volume of the solid bounded by z = 13 - 13(x² + y²) := (x² + y²) ² − 1.

A: The given curves are:z=13-13x2+y2         and           z=x2+y22-1

Q: Find the volume of the solid generated by rotating about the x-axis the region bounded by y = 2.3*,…

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Q: 15 a Find the vector shown above

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Q: Consider the center of mass of the following. A lamina occupies the part of the disk x² + y² ≤ 9 in…

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Q: Find f'(x) and simplify. X x + 36 f(x) = Which of the following shows the correct application of the…

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Q: A volume is described as follows: 1. the base is the region bounded by y = 9 - 1x² and y = 0 2.…

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Q: We need to minimize the cost (measured in units of $100,000) of the pipeline, C(x) = 20✔ 20 5 x +…

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Q: A volume is described as follows: 4 x² and y = 0 25 1. the base is the region bounded by y = 4- 2.…

A: Given the base region is bounded by y=4-425x2 and y=0. ymax=4-425x2max=4 From y=4-425x2 ,x = ±524-y…

Q: Assume that x and y are differentiable functions of t. For the following, find dx/dt given that x =…

A: given  x2+y2=136d dx(xn)=nxn-1d dx(constant)=0

Q: The postal service will accept a box for domestic shipment only if the sum of its length and girth…

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Q: Question 5. The rate of change in revenue from a recently-installed machine is 60,000t + 45,000…

A: The rate of change in revenue from a recently-installed machine is  60,000t+45,000 dollars per year…

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: Evaluate the integral. 3 4x x y cos z dx dy dz

A: triple integral

Q: Answer the following True or False. If f(x) is a positive 1-1 function, then 2πT cb a xf(x)dx = 2π…

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Q: Write an iterated integral for a. vertical cross-sections, b. horizontal cross-sections. da dA over…

A: We have to find the  Iterated integral for vertical cross section and horizontal cross section.

Q: S (3-3sin2x)dx sec2x(cosx−sinx)

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Q: Find the distance from the point (4,-4,-5) to the line a(t) = (3, 1, − 4)t + (9,- 5,3)

A: Given equation of line:- a→t=3,1,-4t+9,-5,3

Q: Q1 :  a) For the function f(x )=x^3 −12x, its local maximum is ____?____ which occurs at (___? __ ;…

A: The given function is: fx=x3-12x   As we know that, The Power Rule: ddxxn=nxn-1

Q: The graph of y=f(-x+1)-2 is drawn below: a) 0 c) Sketch a graph of y=f(x) b) Is the inverse, y =…

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Q: Use the limit definition of partial derivatives to compute the partial derivative of the function…

A: f(x,y)=5-4x+6y-3x2y∂ ∂x(xn)=nxn-1∂ ∂x(constnat)=0

Q: If   C(t)=79.8te−0.13t measures the​ concentration, in ngml​, of a drug in a​ person's system t…

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Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

A: Given: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then…

Q: Find the intervals on which the graph is concave up and concave down. (Enter your answer using…

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Q: Find by implicit differentiation. dy dx dy dx 11 3x² + y² = 4

A: Please see the below picture for detailed solution.

Q: 3, 3, 1 > and b Let a = . Find k so that a and b will be orthogonal (form a 90 degree angle). k=

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Q: Use spherical coordinates. Evaluate III z dv, where E lies between the spheres x² + y² + z² = 4 and…

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Q: Find the volume of the solid that lies under the elliptic paraboloid x/4 + y²19 21 and above the…

A: We have given paraboloid x24+y29+z=1 and rectangle [-1, 1]×[-2, 2]

Q: Let a = - 4i +3j - 5k and b = 5i +2jk. Find - 2a - 36. V

A: a→=-4i+3j-5kb→=5i+2j-kC=-2a→-3b→

Q: Question 18 ( has exactly Show that the equation one real solution. 207e +2023 In z=7²4

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Q: Find an equation of the tangent line to the graph of the function f defined by the following…

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Q: Find the first and second derivatives of the function. g(x) = -5x³ + 10x² + 4x − 64 g'(x) g"(x) =

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Q: Find the inverse Laplace transform L¯¹{F(s)} of the given function. 8s² - 49s + 294 s(s² +49) Your…

A: given  Fs=8 s2 - 49 s + 294s  s2 + 49 and asked to find the inverse laplace transform of F( s ).

Q: Obtain the general solution of the following differential equations 6. xdy - ydx - √√x² - y² dx = 0…

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Q: Find the arc length function for the curve y = sin(x) + √1-x² with starting point (0, 1).

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Q: A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No…

A: Given that , Fencing cost = $14 per foot find the dimension for the plot that would enclose the most…

Q: h(x)=5.5x-3.42

A: We have given a polynomial  hx=5.5x-3.42 Leading term =5.5x

Q: Consider the following. x = ln(t), y = 2t, z = t², (0, 2, 1) Find the equation of the normal plane…

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Q: 1. A tank initially holds 100 gal of brine containing 30 lb of dissolved salt. Fresh water flows…

A: (a) Let x(t) denote the amount of salt in the tank at time t. The rate of change of x is given…