Solve x (az + √2) dx y (az + √2) sin (ay²) dy + (az − √2) dz = 0 4√/2ln |az + √2 = C 4√/2ln|az + √√2|= C 4√2ln |az + √2 = C O a. ax² + acos (ay²) + 2az O b. ax² a cos (ay²) + 2az c. ay² + acos (ay²) + 2az

Q: Find the arc length of the curve on the interval. r(t) = (3 sin(t), 7t, 3 cos(t)), 0 ≤ t ≤ The…

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Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: ㅠ 10. fž sint p cos3 p dp 2

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Q: = Set up the definite integral required to find the area of the region between the graph of y y = 2x…

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Q: = Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: Solve (2y² + 3xy - 2y + 6x) dx + x (x + 2y - 1) dy=0 a. x² (y² + xy b. y + 2x) = C y² (y² + xy + y +…

A: Please see the below picture for detailed solution.

Q: 5. Which of the following functions grows the slowest as x goes to infinity? O 0.01x³ O 0.001x³…

A: We can solve this as follows:

Q: 10. Evaluate f(x) = 10-4x for f(3). a) 23 b) 2 c) 22 d) -2

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Q: f(x) = √x²-2 7+|x6| S if x < 2 if x ≥ 2

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Q: Set up the definite integral required to find the area of the region between the graph of y = 13 –…

A: Concept: Area between the two curves: Let y=f(x) and y=g(x) be the curves and a and b are two…

Q: Evaluate the Integral using the following values. -206 [³x² dx = 260, [°x dx = 10, [° dx = 2 (22-7x…

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Q: 2. d. lim f(x) = e. x-0+ f lim_f(x) = lim f(x) =

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Q: A piece of cardboard measuring 13 inches by 12 inches is formed into an open-top box by cutting…

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Q: nd the radius of convergence, R, of the series. (x + 7)" 7n In(n) = n = 2 nd the interval, I, of…

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Q: 2. The piecewise function g(x) is defined as follows (x+2)³ g(x) = cos(x) (x-1)²/2 if x 1. (a)…

A: Please see the below picture for detailed solution.

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Q: 3. Find the vertex, focus, and equation of the directrix for the conic given by (x + 1)² = -20(y -…

A: We have to find focus, vertex and equation of directrix.

Q: Evaluate are f(4) And solve f(x)=1

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Q: Find the generated volume f(x)=sin(x) and the lines x=0 and x=π and rotate about the x-axis V=π^2…

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Q: Evaluate the triple integral g(x, y, z) dV over solid B. B = {(x, y, z) | x² + y² ≤ 10², x ≥ 0, y ≥…

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Q: Assume that the temperature of a person during an illness is given by: T(t) = 8t/t^2+7 , where T is…

A: The answer is given in step 2.

Q: Find the the e following: sinx first maclaurin four Series nonzero for terms of each (21) S² Tara d…

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Q: f(x) = -2x² + 7 7x 10 - if x ≤ −1 if x > -1

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Q: 00 ΣΤΑ 1 — (−1)n-¹n² 10 Select one: O True O False ≈ 0.0676

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Q: 2. Given the vectors à = (a₁, a₂, a3) and b=(b₁,b₂, b3) show that a × b = -b xã.

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Q: 10. Find the area bounded by the curve x = y² + 2y and the line x = 3.

A: Area Bounded by the Curves : If f(y) and g(y) are two continuous function on a,b and f(y)≥g(y), then…

Q: Given f''(x) = 5x - 2 and f'(-2) = Find f'(x) = and find f(1) - 4 and f(− 2) = 4.

A: Topic = Integration

Q: 2. cotx = sin xsin π 2 --x+cos² x cotx

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

A: The given function fx,y=4x2+8x+7y+3y2 To find the critical points of the function

Q: 8. What is the domain and range of the following relation? y=x²-2x-3 y 5 8 X

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Q: 2. Captain Crunch wants his airplane to travel along a path that is [N60°W] with a groundspeed of…

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Q: 5. Which of the following functions grows the slowest as x goes to infinity?

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Q: The function f(x) = 2x³ - 39x² + 216x 3 has two critical numbers. The smaller one is x = and the…

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Q: d) Hence form a conjecture for the derivative of functions in the form y = (ax + b)². e) Prove your…

A: As you have mentioned I am answering Question (d) and Question (e)

Q: 18. y = 3x + 2 20

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Q: Evaluate [ f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: z = x + y, x² + y² ≤ 1

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Q: a. Find the linear approximating polynomial for the following function centered at the given point…

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Q: Given r(t) = (set, et cos(t), et sin(t)), determine each of the following. (a) the unit tangent…

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Q: 9. Compute the area of the region in the ry-plane wich is bounded by the z-axis and the curve r(t) =…

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Q: 7. Find the equation of a normal to y = x³ - 3x²+x-1 at x = 3

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Q: 2 √9x²-16 x² dx

A: We will use substitute method to solve the integration

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Q: The relationship between temperature and relative humidity in a certain building can be defined by…

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

Q: Evaluate the Integral using the following values. [°x³ dx = 260, [°x dx = 10, [°dx = 2 [°(22-7x-x²)…

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Q: 19. Suppose the rate of change of production of a regular worker at a factory is given by dp…

A: Given problem:- Suppose the rate of change of production of a regular worker at a factory is given…

Q: 2 1 Expand 2y 0.013 2 3. ✓0.0004:

A: Given problem:- Expand 2y210.013y2230.0004

Q: 10. Explain what it means if a. 6 = 0

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Q: 8. Find the equation of the exponential function g(x). (No Decimals) Equation: -6 a

A: Solution ) from the graph  ( 0 , - 2) and ( 1 , 2 ) points are on the graph  Equation of exponential…

Q: Use any method to find the volume, V, of the solid obtained by rotating the region enclosed by the…

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