H.W: Salve the following equations.... 一乂 3. H .... Je A zAyf. (X² 3y)...........

Q: Evaluate the integral 1 Note: Use an upper-case "C" for the constant of integration. 9x² √4x - x² dx

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Q: (b) lim (x,y)→(0,0) x² + y² √√x² + y² + 1 − 1

A: Given limit is limx,y→0,0x2+y2x2+y2+1-1 We need to explain why this limit doesn't exist.

Q: дz (b) Without using implicit differentiation, find where xyz + x-y-z = 1. dx 2

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Q: Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = x - In(6x),…

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Q: If an arc has a length of 3 does this cover an angle less or more than 180 degrees and why?

A: We need to describe arc length.

Q: Find the values of x, y and z that correspond to the critical point of the function ƒ(x, y) = 2x² +…

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Q: Please determine wheather each of the series below converges or diverges and explain your reason…

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Q: Determine whether the integral is convergent or divergent. Evaluate if it is convergent. If you are…

A: Given query is to find the value of the integral.

Q: A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base…

A: Given that side of the square =90 ft.runs with the speed =27 ft/s.Solution :the distance covered by…

Q: 2. In(2x² + y); x = √i, y = 12/3

A: Need to find out the derivative.

Q: Graph the following in polar coordinates (a)  3<r<5,    2π/3≤θ≤4π/3  (b)   r=−8sin⁡θ , Label at…

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Q: 3 2. xdy + y = xy²³ ху dx

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Q: 1+tan^2x/sec^2x-sinxtanx/secx-cos^2x

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Q: = 9,g(-1) = -7, and is h' (-1)?

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Q: Find the maximum rate of change of the function at the point, and find the direction in which the…

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Q: 5. (a) Find the directional derivative of f(x, y) = √√x² − y² at P(5,3) in the direction of v =…

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Q: [2] An isosceles right triangle has an area of A = s² where s is the side length in centimeters and…

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Q: If f(x) is continuous false 2. Assume that f(t) is continuous on [1,5] and that f(1) = 20, f(5) =…

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Q: Please resolve this one.

A: Given integral:- ∫07dxx+13+1

Q: Calculate directional derivatives and gradients in three dimensions. Find an equation for the…

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Q: 9. 11 . + У

A: Note: Since the student has mentioned to solve only question no. (9), so we are solving only…

Q: List all the primes between 20 and 40 in increasing order (in the form 2,3,5,7,9,11). A/

A: I am attaching image so that you understand each and every step.

Q: given cosA=-4/5 with A in QIII and sinB=4/5 with B in QII. what is the value of cos(A+B)?

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Q: [ (x² +1) cos +=dx 2

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Q: Express the given rational function in terms of partial fractions. Watch out for any preliminary…

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Q: Use the degree 2 MacLaurin polynomial of f(x) = cos(2x) to approximate cos(2). . (Enter a number for…

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Q: Evaluate the following integral using partial fraction decomposition. S 12 (x-4)(x+8) 12 (x-4)(x+8)…

A: The given integral ∫12x-4x+8dx We have to find the integral using partial fraction.

Q: 2. Separation of Variables Determine which of the following differential equations are separable. Do…

A: Let's find given diffential equation is separable or not.

Q: π/4 de Evaluate the integral √ (secx + cos x)² dx LENT O blen

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Q: Find r(t). u(t). r(t) = (3t − 6)i + ¹⁄t³j - + 1⁄2 +³₁ + 2k u(t)= t²i6j + t³k r(t) u(t)= 2

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Q: Determine if the improper integral is convergent or divergent, and calculate its value if it is…

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Q: 2. Determine f'(x). (a) f(x) = √26

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Q: Find by implicit differentiation. dx 2x sin(xy³) = x +2y-7

A: As we know that; The Sum/Difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 The Product rule:…

Q: Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle…

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Q: Determine whether the MVT applies to the given f on the given interval. Explain. If so, find all c…

A: Given function  f(x)=x3,           [-1,8]

Q: Ꭱ Find ff f(x, y) dA where f(x, y) = x and R = [0, 1] × [-4, -3]. SSR f(x, y) dA=

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Q: Test each of the following equations for exactness and solve the equation. The equations that are…

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Q: The first derivative of the function h is given by h' (x) = x - x³ + x. On which of the following…

A: Solve by derivative

Q: Use the Laplace Transform to solve the giver initial value problem. y" + 2y + 5y = 0; y(0) = 2,…

A: Given Differential Equation:- y''+2y'+5y=0;y0=2,y'0=-4

Q: X 2. Let z = f(u, v), u = xy, and v= дz (a) (b) Find Find Əz əx and 8²% Əx²* dy " where f has…

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Q: x-y ≤ 0 2x - y ≤ 8 0≤x≤ 11

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Q: Let Find dy || ¹. y = f(x) = arcsin In 7x. dy dx

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Q: Johnson placed $15,000 into his credit union account paying 7% compounded semiannullay. How much…

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Q: Determine whether the Mean Value Theorem can be applied to f on the indicated interval. If the Mean…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 4x³ - 6x² -…

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Q: Solve the given equation.. (x +2)sinydx + xcosydy = 0

A: Given Differential Equation:- x+2sinydx+xcosydy=0

Q: 1. An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

A: Topic -Application of derivatives We are given a cardboard of 20 inch by 32 inch and we need to find…

Q: CSC 3/¹² (3x) cot³(3x)d

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Q: Find the linear approximation of the function f (x, y) x² + y² at the point (2,-1, 1)

A: Given function:- fx,y=5x2+y2

Q: Solve the inequality. State the solution in interval notation: 6x4 + 12x³ < 48x²

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