Write a polynomial f(x) that satisfies the given conditions. 2 Polynomial of lowest degree with zeros of f(x) = X 010 (multiplicity 2) and 5 (multiplicity 1) and with f(0) = 40.

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Q: dy 5: Find for the following functions: dx (1) In (x - y) = xy + y³; (2) y = tan³ √/cot(7x); (4) y =…

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A: Solution : Given that differential equation                  y"-10y'+61=0

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A: Please see the below picture for detailed solution.

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Q: Q2: Find the 1. y = 1- 2. y [In(x² + 2)²]³ 3. y = xcsex tan² (cos x) 4. y for the following…

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Q: (B): If A = 2i + 3j - 4k; B = 3i-4j+ 5k and C = i + j - k, find: (iv) (3A + 4B). C (1) A.B (ii) B.C…

A: The objective of the question is determine the addition and dot product of given vectors.

Q: For f(x) = 7x and g(x)=x+4, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d.…

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A: The given problem is solved below in detail.

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Q: Find the distance between the pair of points (5.5,7.2) and (-0.5,4.2). If necessary, express the…

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

Q: Find the general solution of the differential equation y" 10y' +61y = 0. NOTE: Use c₁ and ca as…

A: find the general solution of differential equation y"-10y'+61y=0

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A: Please see the below picture for detailed solution.

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A: Given: dydx+4y-e-x=0, y(0)=43

Q: Given that 2 ≤ f(x) ≤ 4 for 4 ≤ x ≤ 5, estimate the value of 5 0³/ [ f(x)dx 5 [²₁ <5 f(x)dx

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Q: Consider the region depicted in the following figure. Find the area of R. -1 YA 4- 3+ 2 1 0 -1. f(x)…

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Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³; (2)y=tan³ √/cot(7x); cash? -nh.…

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Q: Solve the following differential equations: (1+x²) (dy-dx)=2xy dx

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Q: Given f(x) = 3x² Rn = 6, find a formula for Rn on the interval [2, 5]

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Q: Q5: Find for the following functions: TTTTTT³ : (2) y tan³√cot(7x) : = (4) y = x sinh 2x-cosh 2x (3)…

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Q: [ 81e-9 sin 9xdx

A: Please see the below picture for detailed solution.

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Q: Q2/ A. Find the following limits. Answer four only. i. ii. iii. iv. V. lim x1 x-1 4x-x² lim X-4…

A: To evaluate the limit.

Q: 15,0-20³²4 2. 3. चं 5. T cos 2x dx sin(³) cos²( :-) / dx 2x - 1 4x dx dx 6. 7. [² (x² + 0²³) dx (x -…

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Q: Find the average rate of change of the function f(x) = x² + 3x from x₁ = 2 to x₂ = 4. The average…

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Q: S 4sin x cos xdx I

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Q: Q4: Answer two only: 4 2 2 1 -1 1 (A): If A = -2 Find AB and AC. 01 0; 2 B = 2 -1 3 -2 -2 and 2 1 3…

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Q: Find the lengths of the sides of an isosceles triangle with a given perimeter if its area is to be…

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Q: Evaluate the following integral. 45 S SS²² dz dx dy -411

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Q: Describe the domain and range of the function. xy x-y z Domain: 0 {(x, y); y # 0} 0 {(x, y): x*y} O…

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Q: (A): solve the following linear equations by Cramer's rule: x + y + 2z = 1 2x-y-z = 0 x +2y-z = 4

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Q: Find the limit. lim (x,y) → (5, 1) ety Discuss the continuity of the function. O continuous…

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Q: · 1. -1 (3-2x) ³ dx

A: The objective is to evaluate the integration.