Determine whether y₁=et, y₂ = sin2t, y3 = cos2t make up a fundamental set of solutions by finding the Wronskian.

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A: Solution :- option 1 is correct .

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Q: Let L be the line with parametric equations x = 2+t, y = 5-2t, z = 4 + 3t. Let S be the plane that…

A: Given L is the line with parametric equations x = 2 + t , y = 5-2t , z = 4 + 3t . Let S be the plane…

Q: For the system of linear equations -3x + 5y = 4 ny + 12x = -16 a) []: Find the values of n such that…

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Q: Questions : 1. Find the 17th term of sequence 3, 9, 27, 81, and so on.

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Q: E = Qui [0₂1] v Day: n RI Month: Year is absolutely continuous. 4 (0) = 4 (T), ü cL ( [0₂T], R^) ]…

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Q: = (k₁) be an m x n matrix with scalar entries. For x € K", let Mx € K™ be defined as n Mx(i) = Σkjj…

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Q: 1) For the vector field F(x, y) =−x²'yi + xy²j, find the following: a) Find the 2D curl of this…

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Q: d ii) Solve the differential equation (D² - 5D + 6)y = x²e³x D = D = 1/2 - dx

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Q: Justify your response thoroughly to communicate your understanding of the concepts. Suppose on an…

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Q: EX: Find the exponential F.5 of the signal shown below, then find the trigonometric form. Sole of(t)…

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Q: Note: Answer all the questions. Ꭷ дуг ď²v 1. (a) If v zlog(x + r) - r, where r² = x² + y², then show…

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Q: 6. A mass-spring-damper system has the equation ma" + ßx' + kx = F(t), where r(t) is th displacement…

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Q: d and e is not solved

A: We already have  A(t)=t23t43-2t-13-t23 and general solution  x(t)=3+t3c1+t2c2-tc1-c2

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Q: max f(x, y, z)=x+2z s.t. x+y+z=1 is (x. y. 2) = (0. - 12/2) with Lagrange multipliers equal to ₁ = 1…

A: Solution of First question is given below:

Q: The price was $450 before 8% tax was added on. What is the price after tax?

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Q: 9- Determine the type and convergence of the improper integral e -2x √2x dr. 3rd type (both first…

A: We have to check the type and convergence of the improper integral ∫0∞e-2x2xdx.

Q: Can the method of undetermined coefficients be applied to the followin DES? a. y' + 7y' - 2y = 3t…

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Q: Six students A, B, C, D, E, and F went to the library once last Monday nigh One of them stole a…

A: according to given conditions A saw B and C B saw A and F C saw D and F D saw A and F E saw B and C…

Q: From which we have (a₁ + a₂) D+ (a3 + α4 + α5) d−(1 − A) (B₁ + ß₂) D² = (1 − A) (B3 + ß4 + 35) Dd…

A: given  D=AD+α1D+α2D+α3d+α4d+α5dβ1D+β2D+β3d+β4d+β5d simplify the terms…

Q: 2. (a) Find Fourier Series representation of the function with period 27 defined by f(t)= sin (t/2).

A: Sol (a) Fourier series of function fx on interval -L≤ x≤ L is defined as: fx=A0+∑n=1∞…

Q: Let X and Y be normed spaces. For F € BL(X,Y), define ||F|| = sup{||F(x)|| : x € X, ||1|| ≤ 1}. Then…

A: There are definitions of norms on bounded linear operators, they all are equivalent.

Q: onsider the following function. f(x) = ln(1 + 2x), a = 4, n = 3, 3.8 ≤ x ≤ 4.2 (a) Approximate f by…

A: Follow the steps.

Q: Quy assume f(x) has the Taylor series write your aswer without rouding 4-2" (x-4)" (24)! h=0 or…

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Q: F(s) = (5 + 3 s+3e = (F(x بر 3² (3+2) 38 +4 F(s) = 2 + 6s + 13)

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Q: Let f: C¹[0, 1] - → K be defined by f(x) = x¹(1), x € X. Consider the sequence {Zn} in C¹[0, 1]…

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Q: 8. Let SR, and recall M= supS is the least upper bound of S. Suppose that S is bounded, so supS E R.…

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Q: Solve: ch= 긍 I/2 برایم (1) -on? To dt

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Q: 8. Given the system dx dt = = Ax with A= 22 5 -1 (a) Find the eigenvalues and corresponding…

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Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and the…

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Q: 4) Find the equation of the tangent plane to the surface r(u, v) = (u²-v²)i − (3uv)j + (4√u+v)k when…

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Q: Which of the following represents the volume of the region bounded by the curves y: = y = 4x rotated…

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Q: 7. Write down the Laurent series of zsin ( (2) about the point z = 0.

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Q: 9. x': 1 1 2 022 -1 1 3 x, x(0) =

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Q: Determine X(S) expressed as a rational polynomial with simplified numerator and factored denominator…

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Q: QUESTION 5 The time till failure of a part, T years, has the probability density function below and…

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Q: Six college sorority sisters-Summer, Autumn, Wynter, June, April, and January-got together for their…

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Q: (b) Use the comparison test to determine whether or not the integral +00 1 x4 + ex dx converges.

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Q: 4. R: y = 2x + 1,x+y = 7,x=8

A: The given curves are: y=2x+1 ,x+y=7 ,x=8   "To find: centroid of the region bounded by the given…