Given the piecewise function defined below, determine the value of 3 f(x)dx in simplest form. -3x² – 1 for x <0 f(x) = -10x for x > 0

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A: Question- A farmer finds that if she plants 75 trees per acre, each tree will yield 45 bushels of fr...

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A: We can find the integration as below

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A: I have stated the used formulas in the solution

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A: Given query is to find the deri at given point.

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A: We have to solve above question 

Q: Solve: 5|x – 1| + 4 > 14 The answer has form: O A B Where A = %3D and B = %3D

A: If x&gt;a then x&lt;-a or x&gt;a .

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A: Given query is to find the number of zeros of the function .  

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A: topic - mean value theorem to satisfy mean value theorem, f must be continuous on closed interval an...

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A: To evaluate the given integral  

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A: for any integer n≥0,∑j=0n2. 3j=3n+1-1

Q: 1- x evaluate the improper integral dx. Does it converge V1 – x2 diverge? Justify your claim.

A:     ∫-111-x1-x2dx=∫-1111-x2-x1-x2dx=∫-1111-x2dx-∫-11x1-x2dx=arcsinx-11-0=π

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A: Let,I=∫ x32-x212dxSubstitute  u=2-x2Differentiate du=-2xdxAnd x2=2-udu-2=x.dxI=∫ x32-x212dxI=∫ x22-x...

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Q: find A-1 using Gaussian elimination and check the resul 3 -2 [1 1) A = |1 2 4. 27 1 1 Ans: A-1 = -2 ...

A: Explanation of the answer is as follows

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A: We can find the answer as below in the following steps

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Q: The differential equation / (xy e ) = y²ež + 2? has a solution of the form f(x, y) = ln |æ| + C. Fin...

A: Given problem:- The differential equation   y' (x y e² ) = y²ey/x + x²   has a solution of the form ...

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Q: nge value of the piecewise function f define- -2 to x = 4. Express your answer in simp 6x for x < 3

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Q: Suppose that we don't have a formula for g(x) but we know that g(1) = -1 and g'(x) = V x2 + 15 for a...

A: Given, g(1)= -1 g'(x)= √(x²+15) g'(1)= √16= 4

Q: Solve for the derivative of the function using chain rule. 8. f(x)= sin (2x)cos (3x)

A: Given problem:- Solve for the derivative of the function using chain rule.   8.     f(x)= sin (2x)co...

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Q: 6. D, (Inx) 7. D, (3x + 4x5) 8. D, (40x) 9. D, (E) 10. D.

A: Find your answer below 

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A: The objective of the question is evaluate the indefinite integral.