Find the absolute maximum and minimum values of f(x, y) = (x^2)y of the set D = {(x, y): x ≥ 0, y ≥ 0, x^2 + y^2 ≤ 1}.

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Q: Find the derivative ofe 11. D[(4x – 5)']

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

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Q: Which is the correct inverse Laplace transform of U (s)=+ O u(t) = 6t + sinh(4t) + cosh(4t) %3D O u…

A: Recall:  L-11sn=tn-1(n-1)! L-1ss2+a2=cos at L-11s2+a2=1asin at

Q: Evaluate F. dr. F(x, y) = 3xi + 2yj C: r(t) = ti + V4 - t²j, -2 < t < 2

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

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Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: Find the exact area under the curve between the indicated values of x. y =x2 - 6x + 9; between x= 2…

A: Solution: ∫24(x2-6x+9)dx

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Q: For the given cost function C(I) = 128/ + find 512000 d) The production level that will minimize the…

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Q: Let 7 (t) = Find 7'(t) F'(t) -

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Q: 1— 2 — е-7 lim 2.x e sin(8x) →-

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Q: Which integral corresponds to the area of the shaded region between the curves y = |a² – 4| and y =…

A: To find the area of the shaded region.

Q: A farmer finds that if she plants 85 trees per acre, each tree will yield 65 bushels of fruit. She…

A: answer is in next step

Q: Find r'(t), r"(t), r(t)•r"(t), and r'(t) × r'"(t). r(t)-흑러 - 26 + (a) r'(t) (b) r"(t) (c) r'(t) ·…

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Q: Verify Green's Theorem by evaluating both integrals an_ am | v² dx + x² dy = dA ây for the given…

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Q: (y – cos?x)dx + cosxdy = 0 %3D

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Q: 2. y = x5 + 2x* + 5x3 + 4x² + x +1

A: Find the derivatives by applying basic differentiation rules.

Q: Since log,(a) = c → a = b°, 1--2 In(즉)- e-1/2. » X = So, y' = 4x(1 + 2 In = 0 when x = -1/2 and y" =…

A: Since logba=c→a=bc                          1=-2lnx5  ⇒-12=lnx5  ⇒e-12=x5⇒5e-12=x⇒        x=5e-12

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Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

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Q: dx 4. Find the integral 2-1)3 a. In (**1) b. In () - + C x-1 2x2-2 + C x-1. 2x2-2 c. - In -+ C 2x2-2…

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Q: Find the area of the region bounded by  y=x^3,y=x+6 and       2y+2=0.

A: This is a problem related to integration. Based on the general formula and concepts we will answer…

Q: Solve the following initial-valued problems. y'=(y/x)+2,   y(1)=3

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Q: r arcsin(5y) dy. Consider the integral V1– 25y? This can be transformed into a basic integral by…

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Q: Find div F and curl F if F(x, y, z) = 8y°z³i – 11x*z°j – 3xy°k.

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Q: An antiderivative for is: 22 +81+20 1 O In + C I+8 ㅇ 올tan-1 () +C 금i미플의 O In 28|+ C O tsec- (4) + C

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Q: Find curl (3z i + 4x j+ 7y k). curl (3z i+ 4x j+ 7y k) = ( i )i + ( i j+ ( )k

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Q: cos(x) sin (x) dx 2 COS V1+ sin(x)

A: ∫cos(x) sin2(x)1+sin(x)dx

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Q: y" + 9y = 9 sec² 3t, 0<t < T/6

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Q: L 3a da = 65 Select one: O True O False 2Vada = 104/3 %3D Select one: O True O False L(z +4)(z +3)dz…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t→+o\ 9t2 + 10' 3t (?, ?)

A: We have to find the limit

Q: Find the area bounded by the indicated curves. y = 3x + 3, y = x2 + 3 Optional For visualization,…

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Q: dy = xe with y(0) = 4 dx

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Q: Find the derivative of F (x) = S (t3 – t)° dt. O 5( – t)* (3t2 – 1) - O (2 - 2) O 5(x³ – 2)* O 3t2 –…

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Q: Find V · (V × F), if F(x, y, z) = 5e²i+ 5xe®j– 7ev²k. %3D V ·(V × F) =

A: We know divergence of curl of any vector v is always zero.

Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

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Q: Total cost from marginal cost. Shelly's Roadside Fruit has found that the marginal cost of producing…

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Q: f(9(x)) = 5 (x + 4) 2 f(g(x)) = (2a² + 3x – 5)7 f(g(x)) = (3x – 1)25 1. - 3.

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. (y - x) dx +…

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). %3D 13 r(t) = e12'i + e'j 156 el4t K(t) : (V144…

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