n Express the function n, lim 21³ n→+∞ n5 i=1 and then find the limit. in closed form

Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: Among all rectangular solids defined by the inequalities 0≤x≤a, 0≤y≤b, 0≤z≤ 1, find the one for…

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Q: SxVx² √x² - 4 dx

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Q: Question 2 Use Euler's method with step length h = 0.5 and determine an approximate value for y(3)…

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Q: Find the general Solution of the complement of the following differential equation y"-y" - y'- 2y =…

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Q: Calculate the line integral of the vector-function F(x, y, z) = (y² +2²) i-yzj + xk along the path…

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Q: 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

A: Given problem:- 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

Q: ) Approximate ſ*^*In(y +1)dy with a midpoint Riemann sum using three equal subintervals. 1

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Q: Solve. 1. Find the equation of the family of curves whose slope at any point (x, y) is 3x. 2.…

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Q: 5. Find parametric equations for the line through the points (1, 3, 0) and (2, 4, 4).

A: The line passing through the points 1,3,0 and 2,4,4

Q: Option 3 + 7 2x2 7 ALL OF THE ABOVE

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Q: VI. Consider the conservative vector field 1. F(x, y, z) = (z cos(rz) -y sin(ry), 2y cos(ry) - ry²…

A: Solved below.

Q: A rectangular metal tank with an open top is to hold 864 cubic feet of liquid. What are the…

A: SOLUTION-

Q: 5. I. Evaluate each determinant. 2 -2 4 L

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Q: dy Write down a differential equation of the form dt 11 solutions all approach y = as t → ∞. 12 y' =…

A: Given problem:-

Q: The region trapped between y = = 4x - 2x² and 4x-2x² |y= ५-२x२-३ = 21² - 1³ y = a) Set up the…

A: The volume (V) of a solid generated by rotating the region bounded by y=f(x) and y=g(x) on the…

Q: Consider the falling object of mass m = assume that the drag force is proportional to the 12 kg, and…

A: We need to choose correct option.

Q: If Vf = F, then F is called a potential vector field, and f is called a conservative function. True…

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Q: find the volume of a solid limited by a cylinder = x^2+y~2=25, by a plane = x+y+z=8

A: Concept: Volume using triple integrals: Let D be a space region that is closed and bounded. Let a…

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: 7. What is the LCM of 16, 24, and 40? O15360 8 O 960 O240

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find each derivative. f(x) = ln sin x COS X y = cos(x² - 2x-8) g(x)=e-In(cos.x)

A: The answers are given below: Topic : Differentiation using chain rule

Q: What is the general solution of the following ODE * (x² + xy − y²)dx + (²x² − 2xy) dy = 0 1 1 x³ +…

A: We know that the equation is of the form of  Mdx+ Ndy = 0  We will check whether the equation is…

Q: Determine the scaler equation of the plane with × -intercept=2, y intercept=-1 and z intercept=3

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Q: Find the area (in square units) bounded by the parabolas x² + 2y - 8 = 0. a. 7.10 sq. units b. 7.01…

A: Here we have to find the area bounded by the parabola.

Q: Solve for y at x=2: (x5 + 3y) dx - x dy = 0; x=1, y=2

A: We need to s0olve D.E.

Q: 3. y = logsin x (csc 4x)

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Q: p(x,y,z)=xz²+sin(y) ex e*

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Q: A rocket is fired vertically upward from the ground. The distances in feet that the rocket travels…

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Q: VII. - ) Let C be the curve consisting of the line segment from (0,0) to (2,0), the the portion of…

A: Given that a curve consisting a line segment from (0,0) to (2,0) and a portion of circle from (2,0)…

Q: TRUE or FALSE: 1. The integer 5047 is a prime numbe

A: To write down that the given number is a primer number or not.

Q: Solve the given differential equation. All solutions should be found. (3y² + 2xy) dx - (2xy + x²) dy…

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Q: Assume that x and y are both differentiable functions of t and are related by the equation y = cos…

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Q: dy dx = x+1 2(y+3)

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Q: 6.) I. Simplify. Write "undefined" for expressions that are undefined. -3 -6 -2 +69 4 -4 6

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Q: Use integration by parts to evaluate the integral. 9x Saxe dx dx = S4x ex

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Q: Question 17 The integral represents which quantity? the total mass with density F the length of the…

A: We need to choose correct option.

Q: Find the critical point of the function f(x, y) = x² + y² + xy +7.5x C=

A: To find the critical point of the function fx, y=x2+y2+xy+7.5x.

Q: 3. I. -1 2 Evaluate each determinant. 5 3

A: Given,-1523

Q: Question 18 If F is a conservative vector field in R³ and C is a loop (curve whose initial and…

A: To find which thing is true about given line integral.

Q: Find the value of the derivative of the function at the given point. 2 f(x) = 3x² − 4x; ( − 1,7) -…

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Q: 1 If sin(0) and is in the 4th quadrant, find cos(0) 8 cos(0) = Enter your answer as a reduced…

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Q: Convert the following differential equation into a Perfect equation and then Find 1+3 general…

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Q: Given: Let B (x, y, z) = (xz, yz, 3x² - z²). 1. The task is to identify the work done by B on a…

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Q: 3) Evaluate f (xy + 2z)ds. C is the line segment from (1,0,0) to (0,1,1).

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Q: I 2. Suppose that z is a function of r and y, and F(x2 - y², ry - 2², yz - 2²) = 0. Calculate and…

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Q: Je(ye-1) dr+e dy, where C' is the semicircle through (0, -10), (10,0), and (0, 10). (Compare Problem…

A: Using green theorem, value is evaluated.

Q: If a rock is thrown upward on the moon with a velocity of 15 m/s, its height (in meters) after t…

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Q: 10 What is the 6th term of (x − 1)¹⁰-

A: Please refer to the image below

Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…