Problem 7. series converges or diverges and mention the test you are using. Show all work. ∞ (b) Σ sin(n) n=1 (α) Σ n=1 Determine if each of the following 52n ∞ (f) Σ n=1 n!(n + 1)! (2n)!

Q: 25-40 Find the critical numbers of the function. 25. f(x) = 4 + 3x – 1⁄2x²

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Q: Determine convergence or divergence of TL A. converges B. diverges Vn 7n +8

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Q: Prove that if a0

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Q: Use the Divergence Theorem to calculate the flux of F across S, where F = zi + yj + zxk and S is the…

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Q: Show that the vector field F = is not conservative by showing it is not path independent.

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Q: Determine whether the following series converges or diverges. Input C for convergence and D for…

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Q: Show that the vector field F = is not conservative by showing it is not path independent.

A: check the conservative of f using curl of F

Q: Solve the following differential equation, subject to the given initial condition. dy x +(1+3x)y =…

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Q: Evaluate the indefinite integral. Use C for the constant of integration. S sin (+) √ 1 + cos(+) d+

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Q: 3. Find tan(t) dt using a u-substitution. (Hint: write tan(t) in terms of sint and cost.)

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Q: the a

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Q: Consider the graph of f(x) to the right. 4 (a) Estimate S 4 [ f(x) dx = [ f(x) dx. 3 (c) If F(0) =…

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Q: Sketch the graph of y = x³ - 6x² + 9x + 1 by first finding the following a) the intervals on which y…

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Q: If f(x, y, z) = 6 √2x+8y +9z, then fz at x = 0, y = 0, z = 1 is =_ 00 -3 01 09

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Q: Q6. Verify that 8²1 əxəy for the function f(x,y) = ln(2x + 3y)

A: Given,            fx,y=ln2x+3yTo find : Verify that ∂f∂x∂y for the given function.

Q: Problem 5: Find the two points on the curve y = 2x² that are closest to the origin. (Explain why x =…

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Q: Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values…

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Q: 2. Find each indefinite integral. Show all steps. c) I ta tan²x sec³x dx

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Q: t on the interval [-3, 0]. 1² +1+1 (Express numbers in exact form. Use symbolic notation and…

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Q: 4) 1z In 4

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Q: 5. Consider the tables of values for the two functions shown. X -2 −1 0 1 2 y = f(x) 9 4 1 0 1 X -2…

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Q: Determine the convergence or the divergence of the series: Σ2inn n=1

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Q: Which interval is f increasing when f'(x) = x³ - x? (a). (-∞,0) (b). (-1,0) (c). (-1,1) (d). (0,0⁰)

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Q: Consider the region bounded by the line x = 2, the curve y = ln x and the x-axis. Setup an integral…

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Q: = = xp (|x|ç - x) Is-x), J 8

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Q: X-fzero(@(X)X^2+3*X-5,(-1.7) X = 1.8541

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Q: B Verify that the Mean Value Theorem can be applied to the function () — 4 on the interval 0,16]…

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Q: dy dx - = C₁emx, where m and C₁ are constants.

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Q: Use differentials to estimate the value of 16.1. Compare the answer to the exact value of 16.1.…

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Q: /3 ㅠ ㅠ Given that 1 ≤ tan(x) ≤ √3 on [1,1], estimate tan(x) dx. 4' 3 < f/3³ tan(x) dx <

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Q: Some ecologists divided a female bird population into three categories: juvenile (up to 1 yr old),…

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Q: 57-58 A particle is moving with the given data. Find the position of the particle. 57. v(t) = 2t…

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Q: Evaluate the integral: 2₂4-2² J O*[] π 2 [1-4] 021-]+0 O O 4T e4 dydx -√4x² ex²+y² +C

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Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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A: we need to graph the functions.