Test for convergence / divergence. Find the limit if result is convergence.

Q: The following statements are true about "Integration" except: the method of adding or summing up the…

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Q: (a) Solve the first order linear ordinary differential equation x sin x + (sin x + x cos x) y = xe…

A: As per bartleby guidelines we only give first question answers.

Q: Let Sketch the curve and find the length of this curve. r(t) = (t, 3 cost, 3 sin t), 0≤ t ≤ 2π.

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Q: 5. Evaluate lim x→2 x² - 16 X x-2

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Q: Q1) Convert the point p = (2,) in the polar coordinate system to its Cartesian coordinate…

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Q: Properties Of The Dot Product (- 2-.. pesta ) n. v = 0 = i = 0 or D = 0or ii 1 v تريلية

A: We have to prove the given property.

Q: 3. How much work does it take to pump the water in a full tank to 2 ft above the tank in the…

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Q: 3z (1-4z-2z²)² dz

A: Given, ∫3z1-4z-2z22dz Formulas used: ∫xndx=xn+1n+1∫1xdx=lnx

Q: Evaluate the double integral: r2 Y To 0 √y¹/3 x7 +1 (Hint: Change the order of integration to dy…

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Q: Find the 1) Sketch the ii) Determine the ::::.) Set-up iv.) Integrate 2 ²) y = x ²²₁₂ y = 2 = x₁…

A: Given problem:- Find the area bounded by curves y=x2 , y=2-x, x≥ 0

Q: √√1-25x² dx

A: This question can be solved by the concept of some special integrals.

Q: Q4. Evaluate : O (xy²) dx dy -√1-(x-1)²

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Q: II. Solve the non-linear equation: 1.) x2 - xy + 2y2 = 16 x-y=2

A: Given:  x2-xy-2y2 = 16        ...(1)x-y =2                         ...(2) To find: The value of x ,…

Q: 5. ft² √1-1³ dt 6. J (2x+3) dx (x²+3x-6)⁹

A: We have to evaluate the integrals.

Q: Which of the following is an appropriate choice for & when proving the following limit? lim(x² - 2x…

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Q: 3. [7.3] Determine the dot product between the two vectors below if there are 135° between them as…

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Q: P 2. ( Use the disk or washer method to find the volume of the solid obtained by rotating the region…

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Q: Please

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Q: Find the solution of the following IVP x²y' + 2xy = ln(x), y(1) = 2 1 1 y = ln(x) y=-In(x) - + 3/2 -…

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Q: Let a(t)=20e^-0.3t ( in milligrams) be the amount of drug in a patients body at time t where t is…

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Q: Which is an equation of a line? A. y = 4 B. x = y^2 -4 C. y^2 = x^2 + 4 D. x^2 + y^2 = 0

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Q: Which of the following are parametric equations for the ellipse given by 9 apply. + y² = 1? Choose…

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Q: 4

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Q: Find the ratio of the length of minor axis to the length of the major axis of the ellipse 9x2 + 16y2…

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Q: If the spherical coordinates (p, 0, ) of a point P are (1, 0,), then the Cartesian (rectangular)…

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Q: S dx -1 x-x² 2³√√x 1423 22 Option 1 Option 3 1425 22 Option 2 Option 4 1521 20 1523 20

A: Given: I=∫-8-1x-x22x3dx   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: USING CYLINDRICAL METHOD Find the volume of the solid obtained by rotating about the y-axis the…

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Q: Let p(t) represent the population of a major city t years after 1950, as shown in the table and…

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Q: 1. Find the Inverse Laplace Transforms of the following. 4 1) -1 S-3

A: The general formula we have that  Laplace transform of eat u(t) is 1/(s-a)

Q: √ √(x²-1)dx

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Q: onvert the point p = (2,7) in the polar coordinate system to its artesian coordinate equivalent, and…

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Q: 1. f(x) = 3x + 2, [−2, 2], ƒ (c) = 5 2. f(x) = x² − x + 6,[1,4], ƒ (c) = 10 3. f(x) = 2/2, [-3,-1],…

A: According to the guidelines, we are answering first three subparts. Please repost the remaining.…

Q: 1. Find the sum of the following infinite sequence: 40, 20, 10, …

A: A detailed solution is given below.

Q: Given f(x,y) = 6x^2 - 2x^3 + 3y^2 + 6xy. Determine any local maxima, local minima, and saddle…

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Q: e the differential equation e2x dy +2e²x y = 2x

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Q: 3) Evaluate f (xy + 2z)ds. C is the line segment from (1,0,0) to (0,1,1).

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Q: Estimate the double integral_R  (3xy^(2)+2x^(2)) dA where R= [0,1] x [0,1] by diving R into four…

A: We need to evaluate integral.

Q: 1. Simplify. Write "undefined" for expressions that are undefined. -3 1-6 0 {}} 4 3 5 3 4.) +

A: To simplify the given expression.To write "undefined" for expressions that are…

Q: Evaluate the double integral: To L 0 y x7 +1 y¹/3 x7 dx dy.

A: The given integral is: I=∫08∫y132yx7+1dxdy   So, The limit of the x varies from y13 to 2. The limit…

Q: tanx - x x-0 x - sinx 1. lim

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Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x + 4) in the interval…

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Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: я f (x) = (x2 + 3x)³ . (4x3 - 5x) 7 - -

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Q: - Solve the linear ODE using an Integrating Factor. x². dy dx + 2xy = 3sin(8x)

A: solution is given below

Q: 1. Find the Inverse Laplace Transforms of the following. 4) 48-60√/s s4

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Q: Find the area of the region bounded by y = 3x - x² and the x- axis. 9/4 9/7 9/2 9/5

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Q: Evaluate S√9-4x² dx a. 0.285 b. 0.123 c. 0.423 d. 0.365 e. NONE OF THE ABOVE

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Q: Given f(x) = x-1 2 on [- 2, 2]. x²+1 a. Find the critical numbers of f on the given interval. b.…

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Q: 6) F(x, y, z) = (xy²z4, 2x²y+z, y³z²) a) Find curlF. b) Find divĒ.

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Q: Evaluate the following limit, if it exists. lim (8-1/2) x→6

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