solve the following couble integrals B) 14 13 2 xy dy dx

Q: 21. a) Evaluate the following limits. Show proper steps. 8x²-2x-3 2x+1 a) lim x→→ 2 2x x-0 √2x+1-1…

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Q: Solve the following autonomous differential equation with the given initial condition. dy dt =…

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Q: Q8. The concentration of a certain prescription drug in the bloodstream after a single dose is…

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Q: Find the gradient of the function f(x,y)=√2x+3y at the point (-1,2). Then sketch the gradient…

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Q: 5. Let G(x) = = = f* tan-¹(s) ds x2 Find G'(x)

A: Fundamental theorem of calculus

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

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Q: , find the range of the function f(x) = 2x² + 12x – 3.

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Q: y= dy xy dxx + 1 with y(0) = 6

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Q: Data released by the Department of Education regarding the rate (percentage) of ninth-grade students…

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Q: If dy = x cos x² and y = -3 when x = 0, when x = π, y = -3.215 2 1.647 6

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Q: 3. Find the slope of the tangent to f(x)=x√√2x² + 17 at the point on the curve where x = -4.

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Q: Determine vector and parametric equations for the line with z-intercept 4 and is parallel to the…

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Q: Let g(x,y)= ln x + 2 ln y-x-8y Find the critical points. Then determine if the critical points are…

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Q: Let D be the triangle in the xy plane with vertices at (-2, 1), (1, 0), and (3, 4). Describe the…

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Q: Evaluate the line integral Jc (2x³y³) dx + (9x³ + y³) dy where C is the unit circle, and verify…

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Q: 2. m, ne N. (a) You are given that limx→ (x log x) lim [xm (log x)"] X→0 Use L'Hôpital's rule to…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Jane is taking a history class. The teacher states that the population of a country is shrinking at…

A: Size of the population, P = 10e0.5t

Q: Determine the exact value (no decimals) of the slope of the tangent line to πT f(x) = −2 sin x at…

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Q: 5. Find the absolute maximum of f(x) = x¹e-77 on [0,4]

A: The given function is,

Q: Write the following expression -3-In(x) - In(y) 3-In(x) + In(y) 3-In(x)-In(y) -3-In(x) + In(y) In XV…

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Q: By using double integrals, find the surface area of the portion of that lies inside the cylinder x²…

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Q: If f(x) = 2x + x ² = O 4.155 O 5.155 O 12.464 O 13.164 2x + x2, what is the average value of f(x)…

A: The given function is; f(x)=2x+x1/2, [0,3]Find the average value of the function.

Q: The graph of f(x) is shown along with the line y = x: Assume that f-1(x) is defined by restricting…

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Q: dy 7. a) Prove that, fo-y4 = 4√/2n e2x b) Prove that, √∞ (e³x+1)² dx: = 2π 9√3

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Q: Find all the second-order partial derivatives of the following function. w=xsin (6x²y)

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Q: 9. Find the points on the graph of y = to the line 28x + 50y - 17 = 0. 7x x-2 where the slope of the…

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Q: If x² + y² = 4, then O false O true dy dx ==3 Y

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Q: Find all the second-order partial derivatives of the function f(x,y) = 3x + 1y+2: 2²f 11 ах'…

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Q: if f(x)= xe^x, determine f^(400) (x)

A: To determine the 400th derivative of the function f(x) = xe^x, we can follow a systematic approach…

Q: Show that dri dt = r2 dr2 r₁ dt. If r₁(t) = t², what is when A₁ = 4A₂? dr2 dt

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Q: For what value of the number k is the following function continuous at r=2 if x 2 f(x) = = (A) 3…

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Q: 12. Compute the derivative of f(x)= = (a) The quotient rule (b) The product rule I for constant n…

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Q: A contour map for a function f is shown. Estimate the value of f(1,12) 30- 20 10- 70 140 2 210 3 280…

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Q: The value of g 28 is -2.269. True False

A: The expression given is,

Q: Let f(x) = In(x) and g(x) = log3x. For all x>1, f(x) < g(x) O True O False

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Q: 3. True/False. Indicate whether each statement is true (T) or false (F). a) b) The derivative of a…

A: To indicate whether each of the following statement is true (T) or false (F).(a) The derivative of a…

Q: Find an equation for the line tangent to the curve y = (√x - 9)(x³. 6) at x = 1.

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Q: What is the area under the graph of y= 32 543-2-1 O 6 NO AU 13 2 12345 4+ -5 155 2 1 2 3 4 5 2 on…

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Q: Find Vf at the given point. f(x,y,z)=x² + y² - 3z²+z Inx. (1,4,3) Vf|(1,4,3)+(+(k (Simplify your…

A: Given:We are required to find:

Q: enter , type P o e field below accepts a list of numbers or formulas separated by semicolons (e.g.…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curve about the…

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Q: B Using the graph above, evaluate the following limit. lim f(x) 42- O PROF (A)1 (B) 2 (C) 3 (D) The…

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Q: Determine the value of h such that the matrix below is the augmented matrix of a linear system with…

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Q: tan (sin ¹(-)) cos (tan ¹(1)) Enter your answer, as a simplified fraction, in the box. What is the…

A: let

Q: A road crew can repave (1)/(48) miles of road each hour. They must repave a road that is (3)/(8)…

A: A road crew can repave (1)/(48) miles of road each hour. They must repave a road that is (3)/(8)…

Q: 2. The minimum depth, d (in meters) of water in a harbour, t hours after midnight, can be…

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Q: Evaluate the volume of the cylinder whose top is the part of hemisphere z = √2 x² - y² in the first…

A: We have to find the volume of the cylinder.

Q: The area of a circle, A, in terms of its radius, r, is given by A(r) = r². The radius in terms of…

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Q: Let f(x, y) = 3x² - 2x + 8y + 5y² - xy List the critical point: The critical point is a Select an…

A: We can find the critical point of the function .

Q: In x (1+In x)² 1. S = dx

A: In this question , we will integrate .