Find the area of the part of the sphere x2 + y? + z² = 4z that lies inside the paraboloid z = x2 + y2

Q: 18. Find the shaded area in the following figure. Assume that there are infinitely many squares and…

A: Area of Infinite shaded region Let Sk be the sum of area of each shaded regionthen…

Q: 2. Consider the sequence (n+2)!. n=1 a. Show that the given sequence is monotone. b. Use the…

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Q: Solue D.E dy + (y cotx Sina) de = o

A: Solving

Q: In(arctan(x)) dx 1 + x2 1

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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: 3. Determine the derivative of each function using the most appropriate notation. (a) y = x³ – 4x² +…

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: Appraximate the critical numbers of the function shown in the graph. Determine whether the function…

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Q: an = In(n+1) – In(n) for n EN determine if the following is convergent or divergent { { an } n=1

A: If an=lnn+1-lnn for n∈N,then to determine whether the sequence, ann=1∞ is convergent or divergent.

Q: Evaluate triple integral ſ´, S,2 ¯* dz dx dy .

A: We can solve this as follows:

Q: Q5) Find volume of body bounded by z = 0 from below and z = 4-x from above inside x = y2 ,x = 4.

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Q: Find the inverse of the given matrix, if it exists. Use the algorithm for finding A1 by row reducing…

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Q: X+ 1 Evaluate lim x→1* ** - 5x +4• | O-1 OO OO

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Q: Find the sum of the convergent series. 1 n vn + 1. n=16

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Q: 1. Evaluate the integral. -1 (6х — 12) dx

A: To evaluate the given integral.∫3-16x-12 dx

Q: Integral using trigonometric sub The answer in the integral is: sin(20) + C 8 4 If x= 2sece then x/2…

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Q: Find the sum of the following convergent series: itan-(2n – 1) – tan-(2n + 3)]. n=0

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Q: Determine whether the following series converges or diverges If the series converges, determine the…

A: The given series is:…

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: given series is convergent 2"

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Q: Find the directional derivative. g(s,t) = s√t , (2,4), v = 3i - j

A: Given:         g(s,t) = s√t ,         Point: (2,4)         v = 3i - j

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: nd the derivative/s of the given item. Final answer should Find if yvx- 8 = xy + 2 %3D dx

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Q: Evaluate the limit, if it exists: x²-9 lim *-3 X+ 3 does not exist -6 1

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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: х2 — бх + 9 dx V6x – x2

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Q: Determine whether the line and plane intersect; if so, find the coordinates of the intersection. (a)…

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Q: 1. The derivative of the sum or difference of two differentiable functions is to the sum or…

A: The solution is given in the next step.

Q: Find the points on the curve y= (x-1)(x -4) where the tangent line is parallel to y= -4x, O (3, 10)…

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Q: 2 3 4 5 1'2' 4'8'

A: topic - formula for sequence

Q: What is the general solution of the system x − 2y + z = 3 2x − 3y + z = 8   Multiple choice…

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (9, –5)…

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Q: 2) Solve the D.E dy + (xy – xy²)dx = 0

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Q: 2. S dx I+,x

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Q: Solve the D.E dy + (xy – xy²)dx = 0 %3D

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Q: 5. What are the coordinates of the centroid of the area bounded by y = x² +2, x-axis (ory = 0), x =…

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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: A bank pays interest continuously at the rate of 6%. How long does it take for a deposit of Q0 to…

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

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Q: x²y(cos(Tz) +2) dæ dy dz

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Q: Determine whether the following series is convergent or divergent full solution pls and write what…

A: Let's find.

Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

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Q: an = In(n+1) – In(n) for n EN determine if the following is convergent or divergent { an } n=1

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Q: Question For the function f (x) given below, evaluate lim f(x) and lim f(x). X00 X-00 V2x8 + 3 f(x)…

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Q: Q2) Solve the D.E xdy + (2y – x* + 3x)dx = 0 %3D

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Q: I c exists in (0, 1) such that f(c) (1)- f(0) 1-0

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Q: (-1)"-1"

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Q: The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

A: Let r be the radius of spherical ballon

Q: Section 6.2 p. 558/560 # 70 In the following exercises, express each series as a rational function.…

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Q: Find an equation of the plane through (-7, 2, –6) that is perpendicular to the planes 4x – y + z = 4…

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Q: Simplify completely 4 Int dt using FTC-1. da e3z

A: This question can be solved using the concept of Fundamental Theorem of Calculus Part 1.