Use any method to determine whether the series converge. ∞ 1 (2) Σ 4k k=1 The series (5) Σ k=1 The series 8 1 4k + 1 < <

Q: Let a = and b = . Find - à - b.

A: Given :a→=5, -5, -1b→=-4, 4, 0

Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √x + 4 and x - 2y + 4…

A: Given problem:- Calculate the volume of solid of revolution when the region bounded by y = √(x + 4)…

Q: The vector a has a magnitude of 7. Its x component is 2, and its y component is twice its z…

A: Given: The vector 'a' has a magnitude of 7. Its x component is 2, and its y component is twice its z…

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y + 15y = 2 sin (3t), y (0)…

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Q: Use the translations to graph the given function. Show all of the transformation on the same graph.…

A: We have to find transformation

Q: 15. Use the results of problems 12,13 and 14 and assume that the Maclaurin Series expansion for ex…

A: We have to prove the given equation of complex number

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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Q: x+3 x ³ + 8x² +16x S da

A: To evaluate the given integral by using partial fractions.∫x+3x3+8x2+16x dx

Q: of the given conditions. lim f(x) = ∞, Sketch the graph of an example of a function f that satisfies…

A: Topic:- limits

Q: -4x 2. Determine an equation for the tangent to the curve y = (x+3)² at x = -2.

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Q: Find the point at which the line x(t) y(t) z(t) - 5+ 5t -6-8t intersects the z plane. - 7+8t

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Q: The area of the region that lies inside the cardioid curve r = cose + 1 and [(cose + 1)² = cos²0]de…

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Q: Find an equation of the line tangent to the curve tan¹(y) = (x+y)e at the point (0,0). tan ¹(xy) =…

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Q: xdx ax + b cos ln x dx X S 2, A = 0

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Q: A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material…

A: Given problem:- A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup.…

Q: 1. The volume of a sphere is given by V = πr³, where V is the volume and r is the radius. If a…

A: Concept: Sphere volume: The volume of a sphere is the amount of space that a spherical can occupy.…

Q: V X if x 3 Find each of the following limits, if they exist. If a limit does not exist, answer…

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Q: log7 X y =(√x) ¹087

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Q: .) Find the limit or show that it does not exist. lim √25t²+2-5t 1-x

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Q: State the order of the given ordinary differential equation. (1-x)y" - 4xy' + 7y = cos x Determine…

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Q: False

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Q: Given f(x,y)=x2y³-4y, find the directional derivative at the point (2,-1) in the direction of v=.

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Q: Find the length of the curve y= 2²-√√x, 4 ≤ x ≤9. 23/2 3

A: To find the length of the given curve.

Q: A Л The path r(t) = (4 sin t) i + (4 cos t) ] describes motion on the circle x² + y2 = 16. Find the…

A: The path r(t)=4 sin ti+4 cos tj

Q: Calculate the direction of P₁P2 and the midpoint of line segment P1P2- P 1(3, 4, 6) and P 2(6, 0, 1)…

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Q: C. Evaluads the Sum 20 [ (₁²+3) ² (

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Q: Find a parabola with equation y=ax^2+bx+c that has slope 4 at x = 1, slope -8 at x = -1, and passes…

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Q: Q1) L-1 s(s²-1) = a) cosht-1 Q2) The general solution of y"" + 2y"-y' - 2y = 0, is: a) y(x) = c₁e²x…

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Q: c) y(x) = c₂x² + ₂x Q20) The form of a particular solution of y"-4y' - 12y = sin(2t), is: . a) y,…

A: Using inverse operator

Q: Given the function f(x) = {2ª 2x x 2 which statement is FALSE at x=2? O The derivative from the…

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Q: Find an antiderivative F(x) of the function f(x) = 7 sin(x) such that F(7) -9. F(x)= = = Now, find a…

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Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √x + 4 and x - 2y +…

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Q: Find the volume of the region of R^3 bounded by the paraboloid z=x^2+y^2 and by the planes…

A: Concept: Let us take D to be a bounded, closed space region. Let a and b represent real numbers,…

Q: 12. etan 2x sec² 2x dx 13. Jdx/(x²-4) 14. (2x¹-x²) dx / (2x² + 1) 15. f (sec²x) dx/(√(1-4 tan² x))…

A: Given

Q: Vector a is expressed in magnitude and direction form as a =(√33, 130°).

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Q: Q17) Evaluate L (2 e-2t sin4t - 0.5 cos3t): 8 S 8 - a) b) (s+2)2+16 2s2+18 (S-2)2+16 252418 c)…

A: 17) To evaluate: L(2e-2tsin 4t-0.5cos 3t)

Q: dh dt k √h(t) ||| h(0) = 2 2 ● T.V

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Q: 4. A 25-ft long ladder is leaning against a vertical wall. The foot of the ladder is on a horizontal…

A: Note : According to our guideline I can solve only 1st , please reroute the remaining question.

Q: Which of the following describes a function? 1. y=x² +1 x=y² +1 1 I only Oll only I and II Neither I…

A: We have to tell about which is showing a function

Q: Solve the following initial value problem for r as a function of t. Differential equation: -=…

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Q: 1) The hyperbolas 6² x ² - a²y² = a) xyy" + x(y²) ²³²- yy²=0 b) xyy" - x (y² 7² - y₁² = c) xyy" - x…

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Q: 3 s²+1 6 s² + 1 Option 4 O * The Laplace transform of the x(t) is x (t) = 3 sint 3 s²+2 6 s²+2…

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Q: l₁: x = 7+2t, y = 2 + t, z = -6 - 3t y-9 Z-13 l₂: 3 - x = -5 -5

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Q: *An Integration factor of the following differential equation dy (x log x) + y = 2log z dx Option 3…

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Q: y = esin(tan-¹ x)

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Q: Solve the following system: 2x + y - 3z = -3 x + 3y - 4z = 11 x + 8y-9z = 5 (2,-1,0) no solution

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Q: Determine the sum of the following series. NOTE: Enter the exact, simplified answer as improper…

A: We have to find the sum

Q: 7. Find the parametric equations of the line passing through A(1, -2, 6) and which is perpendicular…

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Q: 12. Setan 2x sec² 2x dx

A: As per guidelines we can solve only one questions at a time, so if you need more answers kindly…

Q: lim,+1+(1²-2-²-1) In

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