Prove the series diverges through Alternaeting Test. +∞ Σ (−1)α α1/2 α=1

Q: it was estimated that constructing a fence for a project could be done by 11 workers in 15 days. at…

A: Let 'n' be the number of workers. Let 'd' be the number of days required Let WT be the work done…

Q: (√t-9) dt

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Q: 8. Find the area between y = sinx cosx and y = sinx, over the interval 0 <x<T

A: Given y=sinx cosx &amp; y=sinx between the limits x=o to x=πTo find area between two curves:

Q: 9. What is the general solution for the differential equation y"" - 3y' - 2y = 3x? A. y C₁x +…

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Q: Given f(x)=4x+1 and g(x)= x²+x-3: Use the disk method to determine the volume of solid obtained by…

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Q: 4. When solving an auxiliary equation of a certain differential equation the roots m = 1 ± 2j are…

A: I am attaching image so that you understand each and every step.

Q: lim (x-7) tan x x→2 플

A: The objective is to evaluate the limit.

Q: O. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

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Q: 1. For questions A and Given: Radium decomposed at a rate proportional to the qualit of radium…

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Q: = (x² + y² + z²) −½, then + + 8²v მ2u 8² 8x² მ2 82² If v=

A: v=x2+y2+z2-12 Now,  ∂v∂x=∂x2+y2+z2-12∂x       =∂x2+y2+z2-12∂x2+y2+z2×∂x2+y2+z2∂x…

Q: 2.2 5 (2x² – 3x) dx

A: We have to evaluate

Q: II. Solve the following problems. Enclose final answer. 4 4. Given z = Find az/ax x+y "

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Q: 02/Use the l'Hopital's rule to find the limits in t3-4t+15 a) lim t--3 t²-t-12 X-8x² X-00 12x²+5x b)…

A: Given problem:-

Q: nu = ln (2²+2²-²) then x + you is x³+x²y_y²³ Su Su da

A: Homogeneous function

Q: Find the number k> 0 such that the region bounded by the curves y = x² and y = kx has area 9 square…

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Q: 1 -4 The reverse order of SO SAY ex² dxdy is equal to e-1 8e None of them O

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Q: 3. Using the Gauss-Seidel method make three iterations for the linear svstem x(0) = 0, 4x - y -z =…

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Q: Find the integral for the area of the region bounded by y = 2x+4, y = 2-3x, and y = -x using a…

A: Using vertical strip form double integral then integrate

Q: Integrate the equation using the method in trigonometric

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Q: an airplane is moving horizontally at 150 mph over an observer at a height of 4000ft.how fast is the…

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Q: Given f(x)=4x+1 and g(x)= x²+x-3: Use the washer method to determine the volume of solid obtained by…

A: Let's find volume of solid by using washer method when given two curves rotated about x axis.

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A: Given ,  A stone dropped in a pond sends out a circular ripple whose radius increases at a constant…

Q: How far does the car travel during that time? * Onone of the choices O260.133 ft O 300 ft O258.133…

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Q: The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: Let's find rate of area increasing when W=4cm and l=10cm.

Q: Y Calculate y'. Simplify your solution. (x² + 1)² (2x + 1)² (3x − 1)5

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Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 2x³+2x²+2x+6 1. Lim x3+4x+3…

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Q: If A = 2x²,-3yz, xz² and qp = 2z - x³y. Evaluate A Vop and A x Vp at the point (1, -1, 1).

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Q: Find the indicated partial derivative(s). f(x, y) = x¹y² - x³y; Find fxxx and faux

A: Given :f(x,y)=x4y2-x3y

Q: ? Question af Use Mathematica to find the other partial derivative for the function dx f(x, y) = x²…

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Q: The Critical Point of y = xe*

A: Given; y=xe^x

Q: 12. Find the first and second derivatives of f (x) at x = 1.2 and x=2.0 from the following table 1.2…

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Q: For f (x)=xl-2, then f(-2) =0 صواب

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Q: 1. Consider the function f : R² → R such that f(x, y) = 2xy² + x² − 2xy = y + 1. (a) Write down the…

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Q: Given x4 (x + y) = y2 (3x - y), use implicit differentiation to find dy/dx

A: Given: x4 (x + y) = y2(3x - y)

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: We have to find the volume.

Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

A: Using logarithmic function

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A: I am attaching image so that you understand each and every step.

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: We have to solve  part 1, 2 and 3.

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

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Q: For questions no. 2 and 3. Given: A thermometer reading is 60°F at 3:00AM and a Civil Engineering…

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

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Q: Consider a function f whose domain is the interval [a, b]. Show that if |f(x) − f(y)| ≤ (x − y)²,…

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Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 2x³+2x²+2x+6 1. Lim X→2…

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Q: DSX 2 X sec /x dx 3

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Q: Determine the derivative -d/dv y = 2x³ + 5x - 6 y 1 x² 3x 6x³ + x² − 10x − 3 -

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Q: 1. Newton's Law of Cooling: At 9:00PM., a thermometer reading 70°F is taken outdoors where the…

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Q: Find the measures of the angles of the triangle whose vertices are A=(-2,0), B=(3,3), and C=(1,-1).…

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Q: 3/ find the area for the region in the first quadrant bounded by the curve (y = 4x - x²) and line (y…

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Q: 5. Ssin' x dx.

A: I am attaching image so that you understand each and every step.

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: Solid S is bounded by the surfaces z=x2+y2 and z=4-x2-y2