Solve the initial value problem for r as a vector function of t. d²r = - 40k dt? Differential equation: dr Initial conditions: r(0) = 90k and dt = 5i + 5j It=0

Q: 27. f(1) = 1 + e*" 28. f(1) = r² - eW + 5 29. f(1) = (1 + e?)2 30. f(1) = (e' – e")? 31. f(1) = 412…

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Q: y =, x = 1, x = 4, and y = 0 is revolved about the y - axis.

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Q: 1 1. lim x-0+x e*

A: Given: limx→0+1x-1ex-1   So, simply we can write as; limx→0+1x-1ex-1=limx→0+ex-1-xxex-1

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Q: [6]. Consider the following set of parametric equations: x = r° - 3t y = 312 – 9 On which intervals…

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Q: III. GRAPH ANALYSIS: The graph of f is shown below. Use it to answer A, B, and C. -7 -$ -4 -3 -2 1 2…

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Q: Evaluate the following integrals using Trigonometric Substitution: x-1- 16x dx x 2. dx 9 dx 25t2 - 1…

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Q: (-3)"r" ice of the power series Vn +1 n=1

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Q: Use Method of Variation of Parameters: [D2 - 8D + 16]y = e4Xsec2x %3|

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Q: Find the number(s) b such that the average value of f(x) = 6x? 42x +70 on the interval 0, b is equal…

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Q: dr Find de r= 3 sec 0 csc0

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Q: A particle moves with position function s = t4 - 4t3 - 8t2 + 25t, t2 0 (a) At what time does the…

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Q: Show necessary computation x²-9y? lim (x,y)→(1,0) tan-1 (x4 – 4xy + y²) lim (х,у)-(0,0) х-Зу b. а.…

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Q: Evaluate the integral. 1/2 | [6 cos ti-3 sin tj+ sin 3t k] dt 1/2 | (6 cos ti- 3 sin tj+ sin? 3t k]…

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Q: The length of the side of a square floor tile is 15 cm, with a possible error of 0.05 cm. Using…

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Q: B. For each of the following functions z, find and dx²' dyðx' axðy' dy2 1. z = 2x² – 5xy + y²

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: 5. The cost C (in dollars) of producing x units of a product is given by the following. C= 3Vx + 400…

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Q: 00 Determine whether the series omverges absolutely, conditionally, or n=1 not at all.

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Q: Find the area of the plane region bounded by the given curves: y= x, y= 2x, and x+y= 6

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Q: x +729 lim x+9 X-9

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Q: 12. A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 f/sec. Assume the…

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Q: 1 3 5 8 - 37 13) 3 8. 7 Ans. r = 3 0 - 37 0 37

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Q: 6. What type of discontinuity at x = 1 is in the function f(x) =? (A) infinite discontinuity (C)…

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