6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the multivariate chain rule to evaluate af when s= 1 and t = -1.

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A: We need to find f'(x).

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A: We can find the cross product as below.

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Q: Let f(x) = { 2x-3. 3x²+2, if x < 3 if x ≥ 3 be a piecewise function. Evaluate Sof 0 f(x)dx=

A: We can find the integration of the piecewise function as below.

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A: To find out the change in pressure using the differentials.

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Q: 100 100 suppose that Σ a; = -17 and Σ b; = 13. compute the sum. i=1 i=1 100 Σ ( – 30a; – 76;) i=1

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A: Given that fx=x+623a.find f'x=0 and solve x is a critical numbers.fx=x+623f'x=23x+6-13f'x=23x+613so,…

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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all…

A: See this solution in below.

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Q: answer = Σ n=0

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Q: Let a = (5, 5, - 3) and b = ( – 5, 3, 0). Find the projection of b onto a. proj¡ b = <

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A: Please see the below picture for detailed solution.

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Q: Use the rules for sums of powers of integers to compute the sum. 16 Σ k k=7

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Q: ³ [] (2² + y²) p(x, y, z)dV where p is the density function. Moment of inertia about z is calculated…

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Q: If 4x² - y² = 64, show that ds² = 1/2 (15x² (5x² - 16) dx².

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Q: 16. A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x)…

A: We need to find P(x).

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A: Topic = Integration

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A: answer is in next step . please give a like !!

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Q: Determine whether​ Rolle's Theorem applies to the following function on the given interval. If so,…

A: Rolle's theorem states that if a function f(x) is continuous on the closed interval [a, b] and…