7π| A d) S_T/A (sin x + cos x) dx

Q: Compute the average rate of change of f(x) = x2 − 2x on the interval [1, 3]. Find c ∈ (1, 3) which…

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Q: A parabola has an equation of y-32= 0. Compute for the surface area of the solid generated by…

A: Given: y=3x12 At y=0, x=0 The surface area of the surface of revolution formed by revolving the…

Q: 4x+8 (x+2) ³ 3). D. Ba -dx

A: This is a problem related to integration. Based on the general formula and concept we will evaluate…

Q: NIFN dx √2x (√2x + 9)

A: Given query is to find the value of the integral.

Q: √x³√1-x² x2

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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: b) f(x) = хе-пх

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Q: Let g be a function such that g'(x) = x (x - 3). Complete the following arguments to get all…

A: Given, g'(x) = x(x-3) We have to find the extrema from the second derivative test.

Q: 5. Find the limit using any method of choice. x + 2 lim x-2 2x² - x - 10

A: A detailed solution is given below.

Q: Find the second derivative of f(t) = [(1 + 3)¯¹ + 1]¯¹

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Q: 5-x Find the family of the curve whose slope at any point is y-3 passes through the point (2.1) and…

A: Topic:- calculus

Q: 4. Solve each for angles between 0° and 360°. (Round final a steps.) a) cos=-0.2186 b) 5-2 sin0 =…

A: The solution as follows :

Q: Suppose F(x, y) = xyi + (x −y)j and C is the triangle from (4,0) to (-4,0) to (0, 4) to (4,0). (a)…

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Q: To shear a cube-shaped object, forces of equal magnitude and opposite directions might be applied: O…

A: Since, it is given that forces are of equal magnitude but opposite directions and we have to shear a…

Q: 3) Which two vectors are perpendicular? a = [-10, -2, -4] 6= [3,-3, 6] = [5, 1, -2]

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Q: Physical Applications of First-Order Differential Equations A body at a temperature of 50° F is…

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Q: Solve the system of differential equations. = - X1 6x1 + 2x2 X2' - 2x1 - 10x2 2, x₂(0) - 22 = x1 (0)…

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Q: Convert each pair of polar coordinates to rectangular coordinates 1. (1, 60 degrees) 2. (1, 300…

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Q: 7x Find the linearization L(x,y) of the function f(x,y) = e cos (9y) at the points (0,0) and 0, ¹2…

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Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

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Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: (20-0) Given that = 5and 이히 = 3 1 6. Round your answer to one decimal place. = 3 and that (2a ›(à +…

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Q: In5 x ,2 limx→+00

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Q: 4) Given the points A(1, 2, 3), B(5, 4, 3), and C(2, 1, 2), find angle C

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Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

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Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Let the length of a diagonal is = d1=x m So the length of the other diagonal = d2=(x+2) m. Given…

Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² + 1 a. (4,1) b. (2,4)…

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Q: 1. Evaluate the given integral Q. ² = £ Q L² L² (²x - 3) (x - y) dx dy

A: Let I=∫01∫y2yx-ydxdyI=∫01I2dyHere we…

Q: 14. A small, closed water tank is in the shape of a cuboid with a square base. The total surface…

A: Given :Total surface area of cuboid = 1500

Q: Find the gradient of the function f(x,y)=5y-x at the point (8,9). Then sketch the gradient and the…

A: See this solution in below

Q: Find the area bounded by the line y = x+2 and parabola y = x².

A: We can solve this as follows:

Q: x= e-t cos 2t y= e-2t sin 2t given parametric equation find a, b, and c a) find dy/dt b) the…

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Q: Question B2 Consider the vectors, 3 p= and q= 2 (i) Compute 3p - 5q. (ii) Find the length of p, that…

A: A detailed solution is given below

Q: Convert each pair of polar coordinates to rectangular coordinates 1. (2,315 degrees) 2. (1,…

A: 1) We know that relation between cartesian co-ordinate and polar co-ordinates, x=rcos(θ),…

Q: 1. Evaluate the given integral Q. JR (y - 2x) dA, R where R is the region bounded by x = 0, y = x, x…

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Q: A plane that passes through the points A(2,1,1) B(-1,-1,10) C(1.3.-4). Find a vector perpendicular…

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Q: The general solution of y” + 4y = 3 sin 2x

A: Given differential equation, y"+4y=3sin2x...(i) So, corresponding homogeneous equation,…

Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: 2. y = 1 (tanh~' 2x)3

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Q: d. limx→→+∞⁰ 1000 In¹0 X 5 X

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Q: f I. Evaluate tan 2x dx

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Q: 6) A force, F, of 52 N is acting in the direction of a = [2,5] a) Find a unit vector in the…

A: We need to find unit vector and force.

Q: Evaluate the limit tan z lim 20 3x

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Q: x==2t X 1 1-y = Given: line ₁ = -8 and ₂ = = y = 2+2t. 3 2 z = 6 + 2t 1. If the given lines…

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Q: A cylindrical can is to be designed with a capacity of 1000 mL. Find the dimensions of the can,…

A: Given problem:- A cylindrical can is to be designed with a capacity of 1000 mL. Find the dimensions…

Q: sec x = Let f(x) + x³e² - log₂ (5x + 1) + 1 x² √T Using the derivative rules learned in our course,…

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Q: b. lim x->0+ -3/x 2 X²

A: A detailed solution is given below.

Q: Find the binomion coefpicient (7)

A: follw the procedure given below.

Q: 2. F(s): = 1 (S-2)(s-4) (s-8)

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Q: Find the derivative of the function at På in the direction of u. x-y g(x,y) = xy+2¹ Po(1,-1),…

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