Exercise 4.4.5 A thin plate lies in the region between y=x and the x-axis between x = 1 and x=2. Find the centroid. Dow 44

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A: On solving this we will get

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A: Given: I=∫dxx81-x16   ....1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

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Q: b) [. obtained curve 1: Find the volume of the solid by rotating the region bounded by the y = -x² +…

A: Solve the following

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Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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Q: (1) Use the definition to prove that if x → 2 then (2x + 1)/x → 5/2.

A: xn→2 (2xn+1)xn

Q: 16. Use properties of logarithms to expand log (²₁¹). t14

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Q: Question 2 a. I b. | function f(x, y) = y² − x² + — a 1 Find the critical points of the function…

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Q: Find the distance between the points A = (2, 0, (2, 0, 1) and B = (4, 5,-2)-

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A: We have to find the series is Convergent or divergent.  We can apply limit rule to check it.

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Q: 3 √√√x tan-¹ √x dx 1. 1 2. T 3. 3x² + 4x³ +16x² +20x+9 (x+2)(x²+3)² 1 12x+5x+3 4. 0 √ sec¹ x tan³x…

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Q: 22² +52 + 14 (2-1) ¹ If U(z) = CSScanned with CamScanner 9 evaluate u₂ and uz

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Q: `Sketch and find the exact area of the 1) (2 region B bounded by -x y=xe +7, y=x + 9, x =7, and x =

A: As per Bartley guidelines we only give first question answer. Please repost for other parts.

Q: Find the centroid of the region bounded 1 y = 6 sin(x), y ==x, and x = The centroid is at (x, y)…

A: The solution is given below

Q: 2π tane 13-12cose de

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Q: 2e³y - ²x + 2y - 4

A: We will find the critical points.

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Q: Needing

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Q: TRUE or FALSE: Vectors u = (-4, 1, -2) and = 1 7 1 1

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Q: Find the directional derivative of f(x, y) = 3x² - 2y² at point ,0) to point 3 (-2-1,0) 0(0,1). in…

A: Let's find directional derivative.

Q: Integral Calculus (

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Q: In Problems 13-16, graph the constant-cost lines through (9, 9) and (12, 12). Use a straightedge to…

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Q: Consider the region B under the graph of y = 3x² + 1, x = [1,3], and above the x-axis. Find the area…

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Q: Find the centroid of the region bounded by y=x+3 and y=x²-3. O (1.098,1.68) O (0,1.68) O (1.68,…

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Q: Calculate L6 for f(x) = x² + 5|x| over [-1,6]. (Use decimal notation. Give your answer to three…

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Q: Let Find the f(x) = = d Le dt. م الموقع the inter Lo

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Q: Given the following function, f(x) = -2x^3-9x^2+108x-10 , find: a) The critical numbers. b) The open…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost other parts as…

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Q: If f is an even function and fº, f(x) dx = 2 and f f(x) dx = 9, find ſº ƒ(x) dx. (Use symbolic…

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Q: Which of the following is the normal line at the point (-1, 1, 1) to the surface x² – 2y² − 3 ² = −4…

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Q: Find the general solution of the following differential equation. y"+11y12y = 0 NOTE: Use c, and ce…

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Q: Find the limit (if it exists). (If the limit does not exist, enter DNE.) - (x² - -/-) lim

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