Find the derivative of ƒ (x) = 8ª ln (x).

Q: R is the region bounded by the functions f(x) = 3x² + 27x + 54 and g(x) = -3²-22-27. Find the area A…

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Q: mathematically

A: We will solve the problem

Q: 17. √16-e² -dx

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Q: 15. cos³ 3x 3√√/sin 3x dx

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Q: A) None 3 В) 512 Зл 256 3 256 Зл 512 (C) (D) Ε) sin√xcos√x √x E -dx is equal to

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Q: A normal line is a line that is perpendicular to the tangent line which touches a curve at one point…

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Q: 7. f¹ (2x+6)dx ¹x²+2x+5

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Q: ,19 The estimate of an integral of of f(x) dx is given as 1860.9 using 1-segment trapezoidal rule.…

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Q: What is the derivative of −9 sin² (-3x³)? O-162x³ sin (-3x³) cos (-3x³) no correct answer O 162x²…

A: just differentiate the given function by using chain rule of derivative and easily find the required…

Q: Given that dx [2²: = missing steps = [ √x + 2 Re-write the integral will all the missing steps. du =…

A: Rewrite the integral with all missing steps

Q: Solve the given function using chain rule of differentiation. Show your full solution.

A: Given

Q: What is the second derivative of the function y = -6 sin x cos x where x is? Round your answer to…

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Q: Find d²y dx² d²y dx² in terms of x and y. y5 = x6 6 25 X or|c X

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Q: /= 0 sin√xcos√x X Зл A 256 Зл B 512 3 C 256 D) None 3 E 512 -dx is equal to

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Q: Let S be the solid of integration of the given integral Q. (1.) Sketch S and label its boundaries.…

A: Let's solve given triple integral by using cylindrical co-ordinates.

Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

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Q: The plane (x, y, z) = (4, 2, 1) + s(1, 1, -2) + t(2, -1, 3), converted into scalar form, has the…

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Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: Being carefule to allow for parts of the curve being both above and below the x‐axis, to determine…

Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

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Q: Question +² + 1 and g(x) = 2 between x = 2 and x = 3. If R is rotated Define R as the region bounded…

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Q: 8. fx(1+x)²/³ d dx 2/3

A: SOLUTION-

Q: 5. [x3* dx X

A: A detailed solution is given below.

Q: Q3.If f(x,y)=sin(x-3y) + sin(x1 find: af 2x and af dy

A: We can find partial derivative with respect to 'x' and 'y' .

Q: Determine why dx converges or diverges.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: For the following exercises, use the second derivative test to identify any critical points and…

A: First find the first partial derivatives and equate it to zero and find values of x and y. Then find…

Q: Given cost and price (demand) functions C(q) = 110q+40,700 and p(q) = 2q +870, what is the marginal…

A: Here we have to find the marginal revenue.

Q: 2. A lifeguard standing at the water's edge sees a man flailing out in the water. She runs along the…

A: This question can be solved using the concept of trigonometry.

Q: Find using implicit differentiation. Enclose final answers. dx (a) 4x³y² + x¹y³ − x + y = 0 (b) x…

A: 4x3y2+x4y3-x+y=0Differentiating both sides and isolating y' we…

Q: A normal line is a line that is perpendicular to the tangent line which touches a curve at one poin…

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Q: Let S be the solid of integration of the given integral Q. (1.) Sketch S and label its boundaries.…

A: Given

Q: dt ·S₂ (²+1)' 17.

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Q: A company determines that its demand function is given by p(q) = -0.7q+2056 and that its cost…

A: A company determines that its demand function given by p(q)=-0.7q+2056 and that its cost function is…

Q: 3. If ƒ(x) = log₂(−(x − 6)) and g(x) = √(x + ²) a) Determine the domain of g(x) + f(x) b) Is there a…

A: We want to find domain of g+f

Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: The given equation of the curve y=x2+6x+2

Q: Which of the following vectors is equivalent to the vector with magnitude 2 units that is oriented…

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Q: (x - 8)dx x (x + 5)²

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Q: Define as the region bounded by the functions u(y) = √5 + 1 and v(y) = 1 between y = 1 and y = 2.…

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Q: The attached figure shows the surface S1 : y + z = 2 , limited in the first octant with the surface…

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Q: (x - 2y - 1) dy = (2x - 4y - 5) dx

A: Solution:x-2y-1dy=2x-4y-5dxdydx=2x-4y-5x-2y-1dydx=2x-2y-1-52+1x-2y-1dydx=2x-2y-1-32x-2y-1let,x-2y-1=…

Q: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

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Q: Timothy heard that he could triple his money in 27 years if he invested it in his friend's business.…

A: To find the compound interest.

Q: (4x-2)dx x³-X² - 2x

A: We have to evaluate ∫4x-2 dxx3-x2-2x.

Q: dx 1+x-2

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Q: An open-box (top open) is made from a rectangular material of dimensions a = 8 inches by b = 6…

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Q: Determine the derivative of the function g(x) = 3x + 4 / 74x. Do not simplify your answer.

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Q: x² +11x+30 4x+20 For items 37-38: Given the function f(x) = [Select] 37. What is f' (6)? [Select]…

A: Given  f(x) = x2 +11x+304x +20    ------(1)

Q: find the values of λ for which the determinant is zero. 2 λ + 1 0 0 1 O(-1, 1, 1) O(-1, 1, 0) O(-1,…

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Q: 9. √x SOL -√√x dx

A: We will solve the given integral using simple Integration rules.q

Q: St. -4 16-x² A 4 (В 2 (C) 0 (D) None (Ε 8 00 dx is equal to

A: This is based on the definite integral.

Q: 1. Let S be the solid of integration of the ff. integral Q. Sketch S and label its boundaries.…

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