Find the surface area generated by revolving the curve x=y³²-y about the y-axis for 1≤ys 3/2 1/2 3

Q: Prove that √1+i√3+√1-i√3 = √6

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Q: Evaluate the following integral: * *π/2 [sin² 6 1/42 4 O - (2/63) O - (3/28) O 2/63 sin x cos³ x

A: The objective of the question is evaluate the definite integral and choose the correct option.

Q: (y¹x=i+ I 7² +11 -)dx + N(x,y)dy = 0

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Q: 10e²x When x = 0, y = 0, y' = 0 9. (D2+1)y= Ans: y=-2 cos x-4 sin x + 2e2x

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Q: Find the volume of the solid obtained by rotating the region B about the line y = -1. A B

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Q: C 10 A 3 2- 1 1 2 3 4 To find the blue shaded area above, we would calculate: [1(x)d f(x)dx = area…

A: As shown in diagram, lower limit is 1 and upper limit is 2, Therefore a=1b=2

Q: (3x²-3x-4) 2x²-3

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Q: stion T1_Q3 rove by contradiction that there are no positive integers p and q such that 4p²-q² = 25

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Q: Find derivative of the following function. 7x -7x + e y = X

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Q: Find the slope of the normal line to curve x=4sint, π y=cos2t when t=-

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Q: 7. A 25 kg mass is suspended from a ceiling by two cords. The cords make angles of 45° and 70° with…

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Q: Applications

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Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

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Q: Determine the antiderivatives of the following functions: 4. f(3x² +1)4 x dx 5. s dx

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Q: For the line of best fit in the least-squares method,

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Q: (B): Find the integration by using substitution method √x√2x - 1 dx

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Q: Jse the definition of derivative to find f'(x) where f(x)=√x

A: Given,  f(x)=x

Q: Nx - My = R, where R is a function depending only on the quantity z = xy, then the differential…

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Q: A population of animals starts at 484, 000 and grows continuously at 9.00% per year. Find the…

A: Given , Initial population P=484,000 rate r =9% time t=17 year

Q: y=ex5

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Q: Amount of error  Percent of error

A: Given ,  1 cubic inch = 16 cubic cm  True value :  1 cubic inch = 16.39 cubic cm We have to find…

Q: Given an acceleration function a(t)=, find velocity and position functions, given that v(0)= and…

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Q: T (3 sec² x + 4 csc² x) dx 3

A: The given integral,        ∫π3π43sec2x+4csc2xdx

Q: 4. · [ (8x − 3) (4x² – 3x) ³ dx x J dx √1-4x² x ·S dx 3 - 5x² 5. 6.

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Q: 370 0 3sin²2x dx

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Q: 1. A 13-ft ladder is leaning against a house when its base is being pushed towards the wall. By the…

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Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and ƒ'(0) = 8,…

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Q: = 0.3t centimeters per minute 2. The depth of the water in a tank is changing at a rate of r(t) O,…

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Q: 2. Find the coordinates of the y-intercept of the plane (x, y, z)=(4,6,5) +s(2,3,1) + t(3,6,12)

A: To find out the coordinate of y-intercept.

Q: Show that the points form the vertices of the polygon. right triangle: (−4, 5), (0, 7), (2, 3)…

A: The given points are -4,5, 0,7, 2,3

Q: Find the solution of the given initial value problem. ty' + 2y = sint, y() = 9, t>0 y

A: y' +2t y =sin ttEquation is of Bernouli's form:P(t)=2tIntegrating Factor:I.F.=e∫ P(t) dt     =e∫2t…

Q: Find the point of intersection. 4₁:X-17 y-58 z-23 3 2 = 11 L2 x-49 7 N y-26 4 =z-15

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Q: 8. a. Using the vectors x = (3, 3, 1) and y = (-−1, 2, -3), verify that the following formula is…

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Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + B.

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Q: conds after th mem 3) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+32)sin(t)dt

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Q: √4x+4-√√5x+1 x#3 Q18) if f(x)= x-3 k x=3 A) 15) 1 C)O by Q19) Use local linear approximation in ind…

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Q: Find the equation of a circle whose center is at the intersection between the lines 3x - y = 2 and…

A: The standard form of the equation of a circle is x-h2+y-k2=r2 where (h, k) is the center of the…

Q: 1 (2m-3)√4m (m-3) dm

A: Given

Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

A: Let's find volume of solid.

Q: - 13. If u = (4, -9, -1) and v = 4ỉ − 2] + k, determine each of the following: a. u.v f. (2ū+ v) ×…

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Q: Solve the differential equation by the method that you think is most convenient.   (y + √(xy)) dx -…

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Q: Compute the following limits, if possible. You may use L'Hospital's (Bernoulli's) rule if it…

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Q: Find the parametric equation of the line ( x-3, y+6 )•( 2,-3 ) = 0

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Q: Let f(x,y) = 8x - 2y + 5. Find the following values of f(x,y) for the given coordinates. (a) f(2,…

A: Let's find value of given function.

Q: 2. Determine which line is perpendicular to the line 2x-3y + 17 = 0.

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Q: . Determine the area below f(x) = 8x - 2x² and above the x-axis.

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Q: For the function f(x,y)= x + 4y 3 4 x +y find f, fy, f(5,-5), and f,(1,3).

A: For the function fx, y=x2+4y3x3+y4, to find fx, fy, fx5, -5, and fy1, 3.

Q: th which of the following is a Maclaurin series of ) _5. Given the Maclaurin series e* = Σn=0. pr…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Given that f(-10) = -0.1 and f(-9.6) = 1.8, approximate f'(-10). f'(-10) ~ ≈ 94

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Q: Your are driving away from Tulsa. Your distance (in miles) away from Tulsa x hours after 12:00 noon…

A: Given problem:- Your are driving away from Tulsa. Your distance (in miles) away from Tulsa x hours…