Consider the following functions. f₁(x) = 9, f₂(x) = cos2(x), f(x) = sin²(x) g(x) = c₁f₁(x) + C₂f₂(x) + C3f3(x) Solve for C₁, C₂, and c3 so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) (C₁, C₂, C3)=1 Determine whether f₁, f₂, f3 are linearly independent on the interval (-00, 00).

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A: I have stated the used formulas in the solution.

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A: We can express x in terms in terms of y as below.

Q: Q3\ Find the Laplace Transform to the following function L sin2t cos3t

A: Using Laplace transform

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A: As per our guidelines, we are supposed to solve only 3 subparts. Kindly post other parts in the next…

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A: Use fundamental theorem of calculus for finding the derivative

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A: I am going to solve the problem by using some simple calculus to get the required result of the…

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A: We can solve the integration as below using integration by-parts.

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A: The calculation follows easy.

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A: Equate both equations to find limits and intersecting points of these curves

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A: Solve the integration

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A: Solve the integration

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Q: 3. Solve below definite integrals (a) [²3test d (b) ["* dt, 3tedt, ["¹ (c) In(x) -d.x,

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Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then fxy = -10x e5y True O False O

A: A detailed solution is given below.

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A: I =∫xn dx= xn+1n+1 Ans = 1/72

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A: The function is P(t)=0.02(12+2t)3/2+1

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A: Given problem:- Solve the triangle, if possible.   a = 26.38km , b = 21.64km , c = 18.31km

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A: Solution is given below:

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A: Basic partial derivation is used.

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A: Solving the question by finding the value of the problem.

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A: Due to some technical inconvenience I cannot type this answer in Math type I am providing you the…

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A: Topic = Integration

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

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A: We can find the derivative as below.

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A: This question can be solved using the concept of sine rule.

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A: First I have written a property of integral and easily find the True is correct option.

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