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Q: 3. ftan5 4x sec³ 4xdx.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Evaluate. [(-8x¹) dx Determine whether the integral diverges or converges. A. What is the limit? B.…

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Q: Find the length of the spiral r=0², 0≤0≤√21. The length of the spiral is (Simplify your

A: Consider the curve

Q: nction f(x) = (2x-1, x ≤ 1 x², x>1 2 for all x. . tinuous and differentiable for all x. 2x for all…

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Q: Differentiate. f(x) = In f'(x) = : 100

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Q: Differentiate the function. f(x) = log,(xe*) F'(x) =

A: Consider the function Formulas

Q: ind the following limits. -2x³ - 6 x→∞ −5x² - 7x - 8 a. lim -2x³ - 6 x→→∞ −5x² – 7x - 8 b. lim ||

A: Here we will find limit of the given functions, we will find it on putting the x= infinity and -…

Q: Write a polynomial f(x) that satisfies the given conditions. Degree 3 polynomial with integer…

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Q: Please complete parts (d) and (e)

A: To solve part d and part e, answer of part c is required.

Q: For the demand function q = D(p) = 344 - p, find the following. a) The elasticity b) The elasticity…

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Q: A particle is moving with the given data. Find the position of the particle. a(t) t²8t +4, s(0)= 0,…

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Q: Differentiate. y = In (4x² - 7x+5) y' =0

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Q: 5. Find the equation of the ellipse with center at (4, 4), vertices at (4, 10) and (4, -2), foci at…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the directions in which the directional derivative of f(x, y) = x² + xy³ at the point (3, 1)…

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Q: Find the derivative of the following function. y = csc ²0-4 dy 11 ***

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Q: 5 4x +5x7 Find the derivative of the function f(x)=- 2x² 20 (1) Quotient Rule and (2) simplify first…

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Q: Find the derivative of the function. Simplify if possible. y = arccos (e7x) 11

A: Given,

Q: Find formulas for dy and Ay if y = x² - 2x + 1. dy =

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Q: Determine the derivative for each of the following equations. dy dr a.y=sin (8 x) ⇒ b.y = 8 cos (z)…

A: (a) y=sin⁡(8x)

Q: Differentiate d dx y = 11x4 + 3 - (1₁x² + 3) =

A: As we know that

Q: 6. Identify the key points and coordinates (center, vertices, covertices, foci, transverse axis and…

A: The given equation of hyperbola is

Q: A population of 500 bacteria is introduced into a culture and grows in number 4t according to the…

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Q: A plane P contains two intersecting lines given by T₁ = (1, 1,0) +t(1,-1,2) T2 (2,0, 2) + s(-1,1,0).…

A: A plane P contains two intersecting lines given by…

Q: Find three positive numbers whose sum is 160 and whose product is a maximum.

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Q: An ant who is crawling on the ground has its position at time t (in seconds) given by t y(t) = 2+…

A: Given that an ant who is crawling on the ground has its position on time t is given by

Q: 8 3 Evaluate S -dx. 10 9x 4

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Q: Find equations of the tangent plane and normal line to the surface z-4 = ze cos z at the point (-4,…

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Q: 3. Solve the following homogeneous differential equations a. y"-4y'+4y=0

A: To solve the following homogeneous differential equation.Note: Since the student has posted multiple…

Q: 7x 1+2x 2+1 x_3+8 x_4+9x_5 = 69 9x 2+3 x 3+4x_4+4 x 5 = 54 4x 1 + 6 x 2+5 x_4+4 x 5 = 40 2x 1 + 10 x…

A: We solve the following system of linear equations using the Gauss-Jordan Elimination Method:

Q: Find f. f "(0) = sin 0 + cos 0, f(0) = 1, f'(0) = 3

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Q: A = 24 13]. B , B = 0 3-2 4 5

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Q: Find the particular solution of the differential equation x²y" 5xy' +9y=9x (x > 0) satisfying the…

A: To know about Euler's equation:-To calculate complementary factor:-

Q: Solve for x. 4x = 26 Select the correct choice below and, if necessary, fill in the answer box to…

A: The given equation is

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

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Q: A tank contains 1140 L of pure water. Solution that contains 0.03 kg of sugar per liter enters the…

A: The tank has 1140 L of pure water.Solution has 0.03 kg of sugar per liter enters the tank at 3 L/min

Q: 2. a. b. The distance travelled by an object is given by the equation: d(t) = 20t 1+t2 t20. What is…

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Q: Vector w has initial point (2, -1, 3) and terminal point (-4, 75). Which of the following vectors is…

A: Vector  has initial point  and terminal point . To find the vector which is parallel to .

Q: Consider the following equation. cos (y) = 27 Use implicit differentiation to determine an…

A: Given equation, We know,

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

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Q: Determine the equation of the tangent to the graph of y-²-4-√x at the point (4,8). a) y=-7x+36 b)…

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Q: Find the volume of the given solid. Enclosed by the paraboloid Z = 5x2 + 4y2 and the planes x = 0, y…

A: The region enclosed by planes

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: Which of the points P = (-1,4,-7) and Q = (6,-1,5) is closest to the z-axis? OQ (6,-1,5) OQ (6,-1,0)…

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Q: 3. A student is completing a homework problem practicing the method of integration by parts.…

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Q: The definite integral: Use geometry to find (2+√9-x²)dx. a.

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Q: Let A be a 2 x 3 matrix and T: R³ → R² be the linear mapping T (7) = A 7. 2 (6) - A) ¹ (1) - ()-[²]…

A: Consider the linear transformation

Q: If h(a) = h(b), then what is the value of ·b [ g(h(x))h' (x)dx

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Q: 5x+500 A garden shop determines the demand function q = D(x) = 20x +9 the number of plants sold per…

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Q: Compute the value of the following improper integral, if it converges. (If it diverges, enter oo if…

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Q: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting…

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