For the function f(x, y) = (5,-2) that has a positive 2e²* sin(y), find a unit tangent vector to the level curve at the point component. Present your answer with three decimal places of accuracy.

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A: solving the problem by finding the value of the problem.

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Q: 8. Spom INSTRUCTIONS: Find the line tangent to f(x) = sin(ln(x)) at point (1,0)

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

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A: We need to find inverse function.

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A: we can find extreme values.

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A: Disclaimer: Since you asked multiple question, we will solve the first question you. If you want any…

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A: We will find the required derivative.

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A: Topic:- application of derivatives

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A: We have to find the particular solution.

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Q: Find the volume of the solid whose base is the semicircle y = √1 - x² where -1 ≤ x ≤ 1, and the…

A: To find:- Volume of solid whose base is the semicircle y=1-x2 where -1≤x≤1and the cross sections…

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Q: 7. Solve the initial value problem as a linear first-order differential equation: xy' + 2y = 2²-1+1,…

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A: The given equation is x2+xy-y2=4 We have to find the derivative dydx.

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Q: Find an equation for the line that is tangent to the curve y=2x3-2x at the point (-1,0).

A: Given query is to find equation of the tangent.

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Q: (a) Find the arc length function for the curve y = In(sin(x)), 0 < x < , with starting point s(x)= =…

A: Given that y=lnsinx  ,0&lt;x&lt;π   starting point is π2,0To find :Arc lengthSolution :Arc length…

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