What is the center of gravity of the solid formed when the plane region bounded by 2x+y-2= 0, y = 0 and x = 0 is revolved about the y-axis? O (1/2,0) O (-1/2,0) O (0, 1/2) 3 O (0, -1/2) ONA

Q: 1. Answer the following: (a) If you are given a differentiable function f, give at least one…

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Q: Using the shell method, what will be the equation of the volume of the solid formed when the region…

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Q: = ²/² (e ² + e²^²) 3. Obtain the Maclaurin series for cosh x using the fact that cosh x =

A: We need to find Maclaurin series for the function , fx = cosh(x) We know that , cosh(x) = ex + e-x2…

Q: Find the solution of x = X₂ JED -6 where u(t) = 2 and x(0) = [1 -1]. 11 0 JUCE + u(t) (10)

A: The problem is solved using the concept of eigen value and eigen vector.

Q: (b) If A is nonsingular, prove that adj(A) is nonsingular and adj(A)-¹ = adj(A-¹).

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Q: Determine the constants a, p, yo and y'o so that Y(s) = Bs + C (s + D)² is the Laplace transform of…

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Q: For each of the given paths, verify Green's Theorem by showing that dA. Also, explain which integral…

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Q: An ordered field is a field F, and a subset PCF, called a positive set, such that (a) If x, y EP,…

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Q: 1. Answer the following: (a) If you are given a differentiable function f, give at least one…

A: Increment of the function=differential of the function. for small change of x

Q: 13. Consider functions f: {1,2,3,4} {1, 2, 3, 4, 5, 6}. → a. How many functions are there total? b.…

A: Since you have asked multiple questions , we will solve the first question for you. If you want…

Q: 4. Find the center and the radius of convergence of the following power series. 00 2100n n! zn

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Q: Solve the system of differential equations X = = 14x - 6y |y' = 40x 40x17y x(0) = 0, y(0) = −1 x (t)…

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Q: 5. A stone dropped into a still pond sends out a circular ripple whose radius increases at a…

A: Ans: 180πm²sec Explanation: Area of circle = πr².......  A=πr²  ----------[1] Differentiating ....…

Q: Sketch and set up the integrals for volume of the region bounded by y = x^2 + x - 2 and y = 3x + 13,…

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Q: Prove using proof of contradiction. Include explanation.   If n is an even integer, then 7n + 4 is…

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Q: 2. Find the general solution of d²y dy +5- dr.² dx 6y=0

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Q: Using the shell method, what will be the equation of the volume of the solid formed when the region…

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Q: Perform the Laplace Transform | Write Your Final Answer Here * 2e-5t sin 10t + 6e-5t cos 10t

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Q: 14.a Is the function a. EVEN b. ODD f(x) -1, 1, -π< x < 0 0≤x<T

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Q: Date 8. a) Christine just moved into a 2-bedroom apartment. She pays $915 per month in rent. The…

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Q: 3 3 -3 5) Based on the Wave diagram, Find a0. 6) Based on the wave diagram in no. 5, Find bn when…

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Q: (a) Using the formal definition of a limit, prove that f(x) = 2x³ - 1 is continuous at the point x =…

A: The given function is                      f(x)=2x3-1 Definition of limit:  Let f(x) be a function…

Q: Show that the function f(x) = -x²(x + 1)² on (-001 +00) Show that it has an absolute maximum and…

A: f(x) = - x2 (x+1)2       = - x2(x2 + 2x +1)  f(x)= - x4 - 2x3-x2 f'(x)= - 4x3-6x2-2x

Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

A: Given that                   y→=-4-3 and u→=66.

Q: Let I = = {[x] x, y = R} and J = {[2] ZER} E Consider the ring homomorphism y: I → R defined as (a)…

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Q: Consider the equation system: y2 + w2 − 2xz = 0 x3 + y3 − z3 + w3 = 0 Prove that exists surrounding…

A: Given : system of equations   y2+w2-2xz=0x3+y3-z3+w3=0 To prove : there exists surrounding…

Q: Draw a direction field for the differential equation y' = (y — 9)². Based on the direction field,…

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Q: iven the following matrices, solve the questions below and if you can’t solve the problem, explain…

A: This is the question from Linear Transformation.

Q: f(x,y) = (x³ − x)(x² − 1). find fxy(x, ×

A: We have given that ,  fx , y = x3 - x y2 - 1 We need to find , Partial derivative fxy . We know that…

Q: f(x) = = x, over the interval - < x < and has period 27 f(x) [cos cosz+cos3z + cos 5 +... f(x)…

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Q: (5) Show that for any real number x and a subset A of R, exactly one of the following holds: (a) x…

A: Let x is a real number and A be a subset of R then either x will be element of A or x will be…

Q: Determine the Fourier Series of the function below: * f(x) = x, over the interval - < x < 7 and has…

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Q: Let р be a prime such that p = 22" + 1, for some n € N, with n > 1. (a) Determine if 5 is a…

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Q: (3) Prove the Generalized Triangle Inequality: if a₁, a2,..., an ER then la₁ + a2 + ··· + ªn| ≤…

A: We need to prove that if a1,a2,......,an € R  then |a1+a2 +........+an|&lt;=|a1|+|a2|+......+|an|

Q: -3t y" + 6y' + 8y = e−³t - e-5t, y(0) = 0, y'(0) = 0 a. (e³t-1)²e-5t 3 b. (et - 1)³e5t c./ (et -…

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Q: What is the volume in cubic units of the solid formed when the region bounded by (x-1)^2 = 20-4y, y…

A: Given curves are x-12=20-4y⇒x=±20-4y+1y=1y=3x=1

Q: contrapositive proof. Include explanation.

A: Given that if n is an even, then 7n + 4 is an even integer.

Q: 1. Find the general solution of dy dx +y=x

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Q: Find the equation of the line through P = (13, 12) such that the triangle bounded by this line and…

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Q: (1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute…

A: First let xy be positive  Then either both x and y are positive or both are negative  If both are…

Q: Find the general solution of each nonhomogeneous equation. y" + 2y' = 12t²

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Q: Let x, y E Rn be given. (a) If ||x|| = ||y|| = 1 and x y = 1, show that x = y. (b) If ||x|| ≤ 1 and…

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Q: 10. y" + 3y + 2.25y = 9t³ + 64, y(0) = 1, y'(0) = 31.5

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Q: In each of the following problems you are given a function on the interval −π<x<π. Sketch several…

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Q: e moves along line segments from the origin to th F(x, y, z)=z²1+ 3xyj + 2y²k. work done.

A: In this question, the concept of line integral is applied. Line Integral The function to be…

Q: 3. Rhadika earns $600 per week and lives alone in a 1-bedroom apartment. Her monthly rent is $550.…

A: Solution:- Given that, Rhadika earns $ 600 per week and we consider a 4- pay month. Therefore, total…

Q: This exercise assumes familiarity with counting arguments and probability (see Probability and…

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Q: Why is (subtracting two positive numbers that are each less than 1), less than or equal to (1 minus…

A: Since r and s are both between 0 and 1  Then 1-r is positive and also 1+s is positive  Now , take…

Q: lim t→∞ 8 (t²) 4213 +25t¹2 + V t 7835t881t5 + 10t³ 7t²

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Q: 1 2. Σn=10"+ 5n · (Comparison Test)

A: We will use comparison test for series.