37-38 Evaluate the integrals by completing the square and ap- plying appropriate formulas from geometry. 10 37. ·S." 10x - x² dx 38. 8. f.². √6x-x² dx

Q: 1) Calculate the following integrals. b) √₁6x²=1 -dx

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Q: 2. Given the matrix A below, Solve for IAI-¹ A = 23 46 24 135 -1 2 2-3 4874

A: Given the matrix A below, A=123424681357-12-34to solve for A-1.

Q: 2. (4x³-3)dx

A: Let's find.

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Q: Find a critical point tid b.) relative maximum value valve C.) Relative mini mom d.) inflection…

A: Note :-  Here Equation of g(x) = 2x2-9x2+27 =-7x2+27 Or g(x) =2x3 -9x2+27  So we solve this problem…

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A: Given:

Q: 7. ft³10t+-3 dt

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Q: Draw the graphs of the given functions. Find their points of intersection. Find the area bounded by…

A: Given

Q: 5. a) All edges of a cube are expanding at a rate of 3 cm per second How fast is the volume changing…

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Q: Evaluate the iterated integral. [(x + y) dy dx

A: Here is the solution:

Q: 13-16 Sketch the region whose signed area is represented by the definite integral, and evaluate the…

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Q: Find the area bounded by r = 6cos (30).

A: Given: r=6cos3θ

Q: Use a triple integral to find the volume of the given solid. The solid enclosed by the cylinder y =…

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Q: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the…

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Q: a²z a²z Determine + Ər² მ02 if_z = tan-¹ Ө - r + r r²+0²

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Q: 8. Sketch the curves and determine the area of the region formed in the given interval: y = √√2x, y…

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Q: Activity 2: Solve each function below the letters and decode the unknown word in each number. Once…

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Q: The equation below gives parametric equations and parameter intervals for the motion of a particle…

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Q: PH Given: = ln(x²y-1); Find dy/dx.

A: Given xy=ln(x2y-1)

Q: For items 1-5 A 10-ft ladder is leaning against a house on flat ground. The house is to the left of…

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Q: The function given is the population change per year of bald eagles in America P'(t) = 0.21t²…

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Q: 8. For the enclosed regions bounded by y = x² - 6x and y = -2x in the graph, what is the integral…

A: Given   From the graph intersection point

Q: Find the future value of a $20, 000 annual income stream if it is invested immediately as it is…

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Q: 4. Use mathematical induction to prove the truth of each of the following assertions for all n ≥ 1.…

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Q: 10. | x³(lnx+1)8x* dx

A: To evaluate the integral: I=∫xx(ln x+1)8xxdx=∫8xxxx(ln x+1)dx

Q: How many terms of the series do we need to add in order to find the sum to the indicated accuracy? ∞…

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Q: Determine whether the improper integral diverges or converges. 6° x²ex dx converges O diverges…

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Q: csc(x) cot(x) 2-csc(x) a. b. In(2-csc(x)) + C O c. -2 In(2-csc(x)) + C O d. In(2-csc(x)) + C dx…

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Q: Evaluate the iterated integral. [²1²₂(x² - y²) dy d dx

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Q: Find the amount of money that accumulates when a one-time lump-sum investment of P = $50, 000 is…

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Q: 1. A man on a wharf, whose hand is 8.2 m above the level of the water surface is pulling a rope tied…

A: Given;  Rope length =20m Height =8.2m

Q: (a) (c) 1² diz +1 cos(50) de (b) (d) √ X x² + 1 I √x+1 1 dx dx

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Q: Find a, and d for each arithmetic series. See Example 8. wwwww 62. S31 61, S20 1090, 920 = 102 64.…

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Q: Find the future value of a $20, 000 annual income stream if it is invested immediately as it is…

A: Hee, use the formula: FV=erM∫0MS(t) e-rt dt

Q: Find the volume of the solid generated when the region bounded by x = - sqrt(4y) . y = 4 and x= 0 is…

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Q: Find the orthogonal trajectories of the family of curves x² - y² = (² A x² + y²=C² B) xy=C (C) x-y=C…

A: We can solve as follows

Q: Evaluate the following limit using L'Hospital's rule. Provide your answer below: دی lim (4x) X18

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Q: Find T, N and B for the curve F(t) = (2 cos(5t), 2 sin(5t), 3t) at the point t -0 Give your answers…

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Q: What two nonnegative real numbers with a sum of 66 have the largest possible product? The numbers…

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Q: Use the second derivative test to find the location of all local extrema in the interval (2) for the…

A: We can solve as follows

Q: Find the curvature of the curve r(t) = (3 cos (4t), 3 sin(4t), 4t) at the point t 0 Give your answer…

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Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. a. f²f(x) dx y…

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Q: Find the indefinite integral. Solution in handwritten. 1. f(-8x)√3-4x²dx

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Q: Decide whether the integral is improper. [ In(x²) dx proper O improper Explain your reasoning.…

A: Here we have to decide whether the given integral is improper.

Q: Let F(x) = f(g(x)), g(2) = -2, g'(2) = 4, f'(2) = 5, and f'(-2) = 7. Find the value of F'(2). Let…

A: 1st we have to differentiate the given function and  then put the given value.

Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: Given that f (t) = t³e²t sint, which process will yield the less complex and correct Laplace…

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Q: x²-3x - 7 √ - (x² + x + 2)(2x − 1) dx

A: Given: I=∫x2-3x-7x2+x+22x-1dx   As we know that; ∫1ax+bdx=1alnax+b+C

Q: * Find the derivative lic F (+) = (+³-2+ +1) (2+²

A: Given query is to find the derivative of the expression.

Q: Find the length of the parabolic segment r= 6 1 + cos 0 The length is. (Type an exact answer, using…

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