Set up an integral that represents the length of the part of the parametric curve shown in the graph. x = t cos(t), y = t - 6 sin(t),

Q: If lim f(x)=7, which of the following must be true? x→3 f is continuous at x = 3. f is…

A: From the given limit it is clear that the limit exist.Limit exists when left-hand side limit is…

Q: Winter FunⒸ has determined that the total cost (in dollars) for its west coast factory to produce…

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Q: Calculate the derivative of y with respect to x, if x³/² + y-5/2 = 7. dy dx

A: Given equation, .derivative rules:

Q: Solve e³t = 2000 for t. t≈ (Round to three decimal places as needed.)

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Q: The function f(x) = 2x³ − 42x² + 270x - 7 has two critical numbers. Use the derivative to…

A: we are given the function and we need to find the critical numbers.

Q: dy dx - 5ln(t), y = 4t² - 4t-2

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Q: The velocity of a particle moving along a line is a function of time given by 79 t² + 12t + 27 v(t)…

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Q: Match each scatterplot shown below with one of the four specified correlations. O O 00 %%0 O 08 Ⓡ 0%…

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Q: K Evaluate the derivative of the function given below using a limit definition of the de f(x)=x² -…

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Q: Given the demand function D(p) = √100 - 3p, Find the Elasticity of Demand at a price of $17 At this…

A: Elasticity,E(p) = Where D(p) is the demand function.

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: Find derivative of the following function. e³x + e-3x dy dx y = || X

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Q: The hyperbolic cosine function cosh x (pronounced ‘kosh’) is used to describe a catenary, the shape…

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Q: 4 7. Find the equation of the tangent line to f(x) = x5 + √√x³ + v +//w when x = 1.

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Q: Find the derivative of the function. dx y=3e4x²-3 II ...

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Q: The gas mileage m, in miles per gallon, obtained during a long trip is given by m = - Is-551 +15,…

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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: An area to fence is of 37.5 million square feet in a rectangular field.

Q: Solve the separable differential equation for u du dt Use the following initial condition: u(0) =…

A: To solve the following separable differential equation for .

Q: Find all relative extrema of the function. Use the second derivative test where applicable. (If an…

A: The given function is

Q: The figure shows a telephone wire hanging between two poles at x = -20 and x = 20. The wire hangs in…

A: The figure is shown as,The equation for the wire shape is given as,The length of the wire between…

Q: Find the following integrals using substitution. -1 1. fx sin xdx. 2. fcot x In (sin x) dx.

A: To find the following integrals by using substitution.

Q: -. Find dy and Ayat x = 8 with X he exact answers.

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Q: A tank contains 90 kg of salt and 2000 L of water. A solution of a concentration 0.0225 kg of salt…

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Q: Determine the axis of symmetry of the graph of the following parabola. f(x)=5^x2+190x+19

A: To determine the axis of symmetry of the graph of the following parabola.

Q: Find a formula for the nth partial sum of the telescoping series below and use it to determine if…

A: ∑n=1∞(n+6−n+5)

Q: 37. If the region shown in the figure is rotated about the y-axis to form a solid, use Simpson's…

A: The Simpson's rule formula The graph

Q: Set up, but do not evaluate, an integral for area of the surface obtained by rotating the curve…

A: To set up, but not to evaluate, an integral for the area of the surface obtained by rotatng the…

Q: Differentiate. dy dx In x y= 12 X ||

A: we need to find out the derivative of the given function.

Q: Question 3.35) An expert in the housing market tells you that the price of midsize houses in a…

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Q: (a) Let f(x) = arcsin(x). Compute the following quantities. f(1/2) = Number f'(1/2) = Number (b) Let…

A: (a) f(x)=arcsin⁡(x)

Q: K What is the slope of the line tangent to the graph of y=tan(-x) at x = - 4? The slope of the…

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Q: 1. Isolate X.8 (3 + x-4) 4 24+ T (3x + 1 8 = 3x + 1 2x-8 24-9 = X X = 15 T 8

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Q: Find a particular solution to Yp y" - 2y + y = 8.5et t² + 1

A: y"-2y'+y=

Q: / 2 - 100% + A A particle moves according to the equation of motion s = t5 - 10t³ + 18t, where s…

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Q: Consider the function f(x) = x¹ — 32x² +6, −3≤ x ≤ 9. This function has an absolute minimum value…

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Q: The following limit lim Select one: O None of them 8x³y³ (z,y) →(1,2) 2x - y O equals 12. O equals…

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Q: Differentiate y = 11x4 +3

A: given to find

Q: graph f(x - 4) - 5 below

A: given graph of f(x)graph f(x - 4) - 5

Q: Find the derivative of the function g(x) g'(x) = = ex 4 - 3x

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Q: Determine whether C(A - B) is defined. If it is defined, express the result as a single matrix; if…

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Q: Differentiate. g(t)=31t g' (t) =

A: To differentiate the following function.

Q: Suppose the demand for a product is given by D(p) = −4p + 111. A) Calculate the elasticity of demand…

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Q: Find d37 -(sin x). dx37 Derivative:

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Q: Find an equation of the line tangent to the curve √xy+3y=200 at the point (1,64). An equation of the…

A: ......(1)Find the equation of the tangent line to the curve at the point

Q: 2. We found a solution y-sinx for the following differential equation. y"+y=0 a. Use Reduction of…

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Q: 5. Solve the second-order equation xy" +2y' = 12x² by making the substitution u=y'..

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Q: Solve the following homogeneous diffe y"-4y'+4y= 0 »._4y"+л²y = 0, y(0) = 2, y'(0) = 0 x²y" - 2xy' +…

A: Given differential equationwhich is clearly a Euler Cauchy DE

Q: An office machine is purchased for $7400. Assume that its salvage value, V, in dollars, depreciates,…

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Q: Set up an integral for the area of the surface obtained by rotating the given curve about the…

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Q: What is the characteristic polynomial of the matrix A = -24 0 8 -16 0 4 8 8 -20, For ease of entry,…

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