Find all the critical points of the function f(x, y) = x³ + y³ – 9x2 – 21x – y - 66 and label them as either local maximum, local minimum, or saddle points.

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: To evaluate the value of  ∫-∞∞7x2+4x+8dx=7∫-∞∞7x2+4x+4+4dx=7∫-∞∞7(x+2)2+22dx

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A: Find your answer below

Q: Find div F and curl F if F(x, y, z) = 4y®z°i – 11a°z°j – 5xy'k. div F= curl F=

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Q: Question 4 Given the expression below, +. 4rab determine y". Upload Choose a File

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Q: 4. Given that sin 0 =- and let 0 be in second quadrant. 3 7 Find the values for all six…

A: A detailed solution is given below

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Q: Sing do Coso + Cose-2

A: LetI=∫sinθcos2θ+cosθ-2dθPut cosθ=uDifferentiate on both…

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A: Let's find.

Q: The measure of an angle 337.5 degrees is equivalent to ra 15 A 4 15n 8 13п 8 13п D 4. B.

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Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to a or y.…

A: As per bartleby guidelines we only give first question answers.

Q: x+dx Using trigonometric substitution, - (1+x²) = tan odo A sece sin*Ðd0 cose sec 8d0 tan 20 D None…

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Q: Evaluate the integral / (4x + 12y)dx + (15x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: x² – 2 (x + 2)(x + 1)²

A: Partial fraction

Q: 15. Evaluate L s-3 A) 2e e" +t- 61 +t-61° B) 2e " +1-6t -1– 61 C) 2e" +t-3t² D) 2e" +1-3t

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Q: arcsin = ab x² – Va² – y²; Find y'.

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Q: 1. If y = 3x + 2x3 - 3x + 2 find Set A. d'y/dx?

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Q: Use the first fundamental theorem of calculus to find F'(x) F(x) = [ cosr' dt

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Q: Find y': y = arc sec(x²) y = xVx - 1 2 y : xVI -x 2 y = xVx -1 x Vx - 1

A: Given: y=arcsec(x2)y'=dydx=ddx(arcsec(x2))We know that ddx(arcsec(u(x)))=11-1(u(x))2…

Q: Find the conservative vector field for the potential function by finding its gradient. g (x, y, 2) =…

A: We need to find conservative vector field.

Q: dy Given the equation below, find dæ - 51a" + 7a"y + y10 = - 43 dy 172 (15 – 1422y) 29. dæ Now, find…

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Q: k=0 X n-1 The sequence { Xn}, where n20, is defined by Xo = 1 and Xn= E (xx) for n 2 1. The infinite…

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Q: Evaluate the integral.

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Q: n² < 2" for n = 4,5, 6, ... (Hint: 2n + 1 < 2" for n = 3,4, 5, ...)

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Q: Find the third derivative [f"(x)] of the given function: f(x) = 8 sin() %3D

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Q: Consider the points A(1, –3, 4), B(2, –5, 2), C(-1, –4, 2), and D(2,3, –5). (a) Find the volume of…

A: Let a,b,c and d are position vectors of point A,B,C and D resp. Therefore a=i-3j+4k b=2i-5j+2k,…

Q: A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20…

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

Q: Find sin 0. cot 0 = 4 O in quadrant IV sin 0 = (Simplify your answer, including any radicals. Use…

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Q: 1. Find all relative extrema and soddle points of the functon Use econd Partials Test where appli…

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Q: Given the following equation, determine y using the methods discussed in class a - y = cosh(cy) |

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Q: 1. Find the angle between the following two vectors. and

A: The given vectors,  8,-5 and -9,-7

Q: Find div F and curl F if F(x, y, z) = 12y"2³i – 3x"z+j – 4xy°k. div F= curl F=

A: A detailed solution is given below

Q: 1+2x2 dx J x2(1+x?)

A: A detailed solution is given below

Q: Question 2 Differentiate the following function without simplifying y = arc sec(sec(02)) You may use…

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Q: Refer to the given below. Find the indefinite integral. Simplify your final answers (Just like how…

A: i)∫(2x3+12x2-5)dx=∫2x3dx+∫12x2dx-∫5dx                                   =2∫x3dx+12∫x2dx-5∫dx…

Q: Evaluate the definite integrals. (4 significant figures) cosec-4t dt 9. SET A.

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Q: 3. Find y" y = vx² – 4 -

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

Q: Find div F and curl F if F(x, y, z) = 13y'z4i – 16x4z10j – 3xy'k. - - div F= curl F=

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Q: 2. By differentiation rules , evaluate the derivatives of the following and simplify as possible:…

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Q: Find the Maclaurin series for f(r) using the definition of a Maclaurin series. [Assume that has a…

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