Evaluate lim (tan¯¹(t), e-²t, Int) t→∞

Q: (14) Give the appropriate form of the partial fraction decomposition. 2x+32 (x+1)(x+7)

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Q: Calculate the flux of the vector field F = (z, x, y) through the surface S which is the portion of…

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Q: Put the equation y = y = - 3(x + 2)² + 5 into general form y = ax² + bx + c.

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Q: Solve for the particular solution: 4e-3x-2 y' e -6x +3e-3x+2 ; y (0) = 1

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Q: Find the Differential Equation whose general solution is y = C₁e-¹/² + C₂e-4t O 2y" -9y' - 4y = 0…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Concept check: Evaluate the following integrals and use the appropriate transformations when needed.…

A: Need to find out the integration.

Q: Find the smallest nonnegative integer for x such that x = 2 mod 3 x = 3 mod 5 x = 2 mod 7. A

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Q: Tlake Home part of lest 1. Find the critical values. for f(x) = x² + 4x³+4x²

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Q: A particle moves along the curve implicitly defined by xy¹ - yx4 = x-y2. When the particle passes…

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Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 25 m/s, its height…

A: The given data is: h=25t-1.86t2 Initial velocity u=25 m/s (a) To find the velocity of rock after 4 s…

Q: The volume V of a growing spherical cell is V= r³, where the radius r is measured in micrometers (1…

A: We have given V=43πr3, where r is the radius and V is the volume.  a) find the average rate of…

Q: Evaluate S COS 3 ³ (1) 6 [ cos ³ (1) dx = 3 6 dx.

A: Given query is to find the integral.

Q: Find the exact value of each trigonometric expression. For each part state the quadrant or axis that…

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Q: An implicit function has a vertical tangent line if = 0. Find the four points on the implicitly…

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Q: Determine the least possible degree of the polynomial function shown. The least possible degree…

A: We know that polynomial has degree n if it has n x intercept and polynomial has degree n if it has…

Q: Find the indefinite integral using the substitution x = 5 tan(0). (Use C for the constant of…

A: Topic- Indefinite integral We are given,∫x525+x2dxx=5tan(θ)

Q: f(x) X 2 tan r -

A: We have to solve given Questions.

Q: Use the Laplace Transform to solve the given initial value problem. y" - 2y' + 2y = cos t; y(0) = 1,…

A: Let's solve given diffential equation by using Laplace transform.

Q: What term(s) should appear in the partial fraction decomposition of a proper rational function with…

A: Topic - Partial fraction decomposition We are given, a.) A factor of x-3 in the denominatorb.) A…

Q: If g(x)=xf(x), where f(3)=4 and f'(3)=-2. 1. Find an equation of the tangent line to the curve of g…

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Q: d Perform the following Operations on the | 14 = (-2₁-3₁-5), V = (4₁-2₁-1) to W² = (-404) R₁W = [ (u…

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Q: x)/(x^2+1)  Use a TABLE to show intervals in which f (x) is increasing or decreasing, concave up or…

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Q: Calculate the first four partial sums of the given series, S₁, S2, S3 and S4. Also, determin whether…

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Q: Give the appropriate form of the partial fraction decomposition for the following function. 5x (x -…

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Q: Let y=tan(5x + 4) Find the differential dy when z = 2 and da= 0.3 Find the differential dy when - 2…

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Q: 2. The area of Mammoth Cave Nationc Park in Kentucky is about seventy-four thousand, nine hundred…

A: We have given the area of the which is "Seventy-four thousand, nine hundred thirty and sixteen…

Q: Concept check: Evaluate the following integrals and use the appropriate transformations when needed.…

A: Given integral:- ∫cot4t2dt

Q: f(x) = e* (tan x - x - x²)

A: We can find the derivative using product rule in the below steps.

Q: Evaluate the integral 10 10 sin(x) cos(x) Note: Use an upper-case "C" for the constant of…

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Q: Use logarithmic differentiation to find the derivative of y = (In(4x))(5x) (where x > 1/4 so that…

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Q: cos8x-1 sin8x 4.Evaluate y' for y=- and simplify the answer

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Q: ive the appropriate form of the partial fraction decomposition for the following function. 9x² +7…

A: The given function is 9x2+7(x2-6x+9)(x2+4x+5)

Q: 66. 1 - 1 2 + 2 4 68. + 5 25 1 4 + T 8 125 +

A: Question no. 66 & 68 solved

Q: Find the derivative of: - R(t) = (sin² (3t+1), ln(t² − 1), ²) +1

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Q: Evaluate the following integral using partial fraction decomposition. S 12 (x-4)(x+8) 12 (x-4)(x+8)…

A: The given integral ∫12x-4x+8dx We have to find the integral using partial fraction.

Q: If R(t) = et costỉ - et sin tj Find the speed, tangential and normal components of acceleration when…

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Q: Use the properties of logarithms to exapnd the logarithm as much as possible: 4 log5 ພາ2 x4y³

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Q: Suppose that a fourth order differential equation has a solution y = - =-6e5x (a) Find such a…

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Q: Solve the equation with homogeneous coefficients. (x² + 3xy + y²)dx - x² dy=0

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Q: Find the dimensions of a rectangular corral split into 2 pens of the same size producing the…

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Q: 1. An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

A: Topic -Application of derivatives We are given a cardboard of 20 inch by 32 inch and we need to find…

Q: 2x²-5x-10 (x+2)(x² −4) dx

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Q: Consider the following. 7x²y³ = 8 (a) Find y' by implicit differentiation. 14x 3y y' = (b) Solve the…

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Q: Use logarithmic differentiation to find the derivative of y = sin(5x)1+5x; y = 5*(1+5*x)*sin Your…

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Q: Find the Wronskian of the given pair: e4t, e-3t/2 (11/2)^(5/2) O (5/2)^(5/2) -(5/2)e^(5/2)…

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Q: Given the following graph of a function. 2 What is its domain? O 4 0 (-∞0, +∞0] O (-∞0, 2) U (4,00)…

A: We start at the far left side of the graph. We notice the arrow of the blue graph indicating the…

Q: - ƒ(x) = (x² + 3x) (x−¹ − x¯4)

A: ddxx2+3xx-1-x-4

Q: b) Find the differential of the function f(x) = tan(√x)

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Q: Parameterize boundary of triangle (0,0),(5,0),(3,9)

A: We can parameterize the triangle in the below steps.

Q: one has a Tess man its polynomial function. The volume of a cone is V = ²h for radius r and height…

A: Given query is to find the volume of the function.