9. (D² – 2D + 5)²y = 0 10. (D² – 2D – 3)y = 0 when x = 0, y = 0, y' = –4 %3D -

Q: Q2) Solve the D.E dy + (xy- xy?)dx = 0 %3D

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Q: In a certain year, 89% of all Caucasians in the U.S., 75% of all African-Americans, 75% of all…

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Q: Is it a function? 4 12 yes or no -1 -3 -4 -5 -21 Explain. 1 -3 4 12 -2

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Q: Question A 13-foot ladder is leaning against a wall. If we pull the ladder the wall at a rate of 6…

A: topic - application of derivatives

Q: Consider the tollowing Maclaurin series: (-1)"x²n (2n)! CoS X = for all x E R. 1. Let f(x) =…

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Q: Σ (-1)" n=1 3-4n-1

A: topic - geometric series

Q: (-1)" V2n2 + 5 n er series (x + 1)" n=1

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Q: pln e" sec? e" dx In 플 Find (a).

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Q: x² – 6x +9 dx 6x – x2

A: Here we have to find the integration.

Q: Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3rVx+ 2 10 4. -…

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Q: Determine if the improper integral converges or diverges. Find its value if it converges. Show…

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Q: x² +2 dx (x – 2)(x² – 2x + 2) 1. -

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Q: /2n?

A: The given series is: ∑n=1∞(-1)n(-1)n2n2+5=∑n=1∞(-1)2nn2+5n2=∑n=1∞1n2+5n2

Q: ind the point of intersection (xo, yo, zo) of the lines given as: L: x = 2 + t, y= 4+5t, z = 5 +t L:…

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Q: Graph the function. Show at least one period. 15) y = 2 sin (2ax - 3)

A: the graph for given function is attached below:

Q: Differentiate the following function and factor fully. g(x) = (2x – 1)*(2 – 3x)“ |

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Q: Question You are stationary on the ground and are watching a bird fly horizontally towards you at a…

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Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 7,…

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Q: Find the smallest number n of terms needed to obtain an approximation of the series 27ke-0.254² k=1…

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Q: Use the first principles definition of the derivative to find f"(2) where Ax) = O a) 0.125 b) 4 c)…

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Q: Find the volume of the following solid. The tetrahedron bounded by the coordinate planes (x-0, y= 0,…

A: Given problem:- Find the volume of the following solid.   The tetrahedron bounded by the…

Q: Find the area of the band cut from the paraboloid x² + y² – z = 0 by the planes z = 2 and z = 6.…

A: To find the area of the band cut from praboloid.

Q: Question Use the Second Derivative Test to find the location of all local extrema in the interval…

A: We have to find the extreme points.

Q: ) Solve the D.E dy + (xy – xy²)dx = 0

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Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 6z + 18 =…

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Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 13.…

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Q: Consider the parallelepiped with adjacent edges u = 9i + 5j + k v = i+j+ 8k w = i+ 2j + 8k Find the…

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Q: (a).x = 61, y = - 4 + 7t O (r, y) = (0,4) + «(6, 7) ai + bj = 4j + 1(6i + 7j) O (1, y) = (6, 7) +…

A: topic - equation of a line

Q: Let f : [a, b] R be a continuous function on [a, b). Prove that if |f(x)| dx = 0 then f(r) = 0 for…

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Q: 3-x Q1) Evaluate the integral * dy dx using polar coordinate

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: What is the shortest distance from the point (4,0, 5) to the sphere (x – 1)2 + (y + 2)2 + z² = 36?…

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Q: a ) Σ-1 (-1)"-1 Zn=1 2n+1

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Q: Sketch the region in the plane consisting of points whose polar coordinates satsfy the given condi-…

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Q: æP In(x) dz a. Find the values of p for which the integral converges. The integral converges for all…

A: ∫01 xplnxdxApplying integral by parts,=1p+1xp+1lnx01-∫01xpp+1dx=1p+1xp+1lnx-xp+1p+1201=-1p+12…

Q: PART II. Find the derivatives of the following expression, solution must be presented. (3 marks…

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Q: Consider the tollowing Maclaurin series: (-1)"x2n (2n)! COS X = for all x e R. n=0 1. Let f(x) =…

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Q: n+1 n+1

A: As per the instruction, we will be answering only the first one. For (1),     limn→∞…

Q: Find fy (x,y) if f(x.y) = (x° +y®)* fxy (X.y) = %3D

A: Topic = Derivative

Q: Q3) Evaluate triple integral dz dx dy.

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Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

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Q: 22n Σ (2л — 1)". - Vn² + 1 3 n=1 Use limit comparison test to show that the given power series is…

A: Solving

Q: d -sin 6 if0 is given as dx What modifications would have to be made to find the derivative an angle…

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Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 4 cos(t) -…

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Q: Find f. f"(x) = -2 + 24x – 12x², f(0) = 6, f'(0) = 16 %D %3D f(x) = –x4 + 4x° 3 x + 16x + 6 %3D

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Q: In 4x 5. S dx

A: The integration of the integral is ln(4x)/x.

Q: Problem solving: 1. What is Ax in this expression? 72 4 lim (3+ - 7200 i=1 4i C. : 41 D. A. (3 + )*…

A: As per guidelines, I can answer maximum one question and three subparts of a question. Since you…

Q: sin7t sin4t dt =- 121 – cos 31) dt A) True B) False

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: Find the area of the triangle with vertices P(1,2, –5), Q(0,0,0) and R(2, 4, 1). NOTE: Enter the…

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Q: Find an equation of the plane that is parallel to the plane x + 2y – 4z + 16 = 0 and contains the…

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