Find the limit of the following:  a) lim x→∞ (sin2x / x2) b) lim x→∞ (x - √x)

Q: 3. Determine whether the following function y=c₁x + ₂x³ + 2x²e* - 2xe* is a solution to the…

A: We have to determine given function whether solution of given differential equation.

Q: The solution of the differential equation x = y + (1 + ln y − Inx) is: dy dx

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Q: 4. [secx tan x cos(secx) dx

A: A detailed solution is given below.

Q: Complete the following table. Exponential Form 1.2¹ = 16 2. 11² x 3.7%= 400 5. 6. 7. 8. 16¹/4=2 9.…

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Q: ind the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Given: y=8x3,y=0,x=1 about x=2

Q: 1. Consider the ODE: (2x + 4y) + (4x − 2y + 1)y' = 0. Verify that the ODE is exact and then find its…

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Q: Use a tangent plane at (-6,-4) to approximate the value of the following function at the point (-…

A: Given function :  −2x2−4y2+7z=−101 Now, −2x2−4y2+7z=−101z=2x2+4y2−1017f(x,y)=2x2+4y2−1017

Q: Find the differential dy of the given function. (Use "dx" for dx.) 6 √x dy = y = 9√√x +

A: Formula we use d(xn)=nxn-1dx. d(f+g)=d(f)+d(g).

Q: F(x,y) = 5 x³ ty sin²x 4 2 x +y 0 if (x,y)=(0,0) " ‚ if (x,y)=(0,0)

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Q: 393. √3V1 + x²

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Q: Find the curvature of the curve y = 4e-4. a) Ok= b) Ok= c) Ok= d) Ok= e) Ok= 64 e 4 x (1 +…

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Q: (A B Which of the following functions satisfy x²dy + y(x + y)dx=0 with y(1) = 1 ? 3x²y = 2x + y x²y…

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Q: ind an equation of the plane passing through the points (-1,2,0), (2, 3, 6), and (-1, 0, 2). Use…

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Q: Find the limit if it exists. If the limit doesn't exist explain why (assume a = 0) a — |x| (c) lim…

A: To find the limit.

Q: 5. 2w² - 5w+ 11 = 0 6. 7q²-3q + 1 = 0

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Q: What is a singular matrix

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Q: 3. f(x) = -2 x+1

A: The function is  f(x)=-2x+1

Q: 4. y= x+1 X 5. Y = √4x+3

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Q: Find the Range of 1/√x³+8

A: We can find the Range of the function .

Q: The solution of the differential equation y': || x 1 + 1 is:

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Q: Given: (x is number of items) Demand function: d(x) = 264.5 0.2x² Supply function: s(x) = 0.3x² Find…

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Q: Which of the following equations is a linear differential equation? (choose all possible answer) A В…

A: The given differential equations are,

Q: Can we use x = vy? (x -y In (y/x)) (vy - y In(y/vy)) --> (vy - y In(1/v))

A: yes you can do it.

Q: Find the point of intersection of the lines below. Then find the equation of the plane containing…

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Q: express each common fraction as a decimalfraction. Round to four decimal places when needed. 3⁄20

A: Given expression, 320

Q: Evaluate the integrals S 1 x2-7x+10 dx

A: As per the company rules we are supposed to answer only the first question and rest other can be…

Q: Use differentials to approximate the value of the expression. Compare your answer with that of a…

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Q: Use the price-demand equation p +0.05x = 100, 0≤p≤ 100. If p= 35 and the price is decreased, will…

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Q: Graph the given functions, f and g, in the same rectangular coordinate system. Describe how the…

A: All the parts are solved below in detailed manner.

Q: 1. Verify that the conclusion of the Clairaut's Theorem hold d) z = ex cos y e) z = sin x sin y

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Q: Determine the degree of the differential equati 3/2 2/3 (3x² ² 2 + 4xy) ¹ ² = (2y³d² - 4xy)" d²y dx²…

A: The given differential equation is; (3x2d2y/dx2 +4xy)3/2=(2y3d3y/dx3-4xy)2/3

Q: The figure shows the position versus time curve for an ant that moves along a narrow vertical pipe,…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: (1, 1) 183. x=5y3/2 from y = 0 to y = 1

A: We need to find arc length. NOTE - As per Bartleby's guidelines we can solve one question from…

Q: N 1/2 + x ) d x Z

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Q: Which of the equation: Show your A. following is the general solution of the differential X ady - y…

A: The given differential equation is; x3dy - y(x2-y2)dx=0

Q: please solve   401,411

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 2. f(x) = x1/2₂ -2 3. f(x) = -2 x+1 4. y= x+1

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Q: Given the system of linear equation below, determine the value of x, y, and z using: a) Gaussian…

A: The solution is given below

Q: Find a plane containing the point ( – 2, — 1, − 2) and the line of intersection of the planes − 3x +…

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Q: F (N) 24 18 12 16 2 00 4 6 8 10 12 14 16 x (m) How much work W is done (in J) by the force in moving…

A: Topic = Area

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: A small business can produce a maximum of 54 of its product per month and sell them for $ each. The…

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Q: Given the function f(x):  f(x)= x^2 + 1 , − 1 ≤ x < 0          2x− 1 , 0 < x < 1          1 , x = 1…

A: Given the function f(x): f(x)= x^2 + 1 , − 1 ≤ x &lt; 0         2x− 1 , 0 &lt; x &lt; 1         1 ,…

Q: (a) Evaluate the following. If the limit does not exist, explain why. lim f(x) = 3 4-0 lim f(x) = 1…

A: Graph of the function is given, we have to find the given limits.

Q: Use the Shell Method to compute the volume of the solid obtained by rotating the region in the first…

A: Use the Shell Method to compute the volume of the solid obtained by rotating the region in the first…

Q: A function is given. f(x) = 7x − 8;    x = 2, x = 3 Determine the net change between the given…

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Q: 1. Find an equation for the set of points whose distance from the point (1, 2, 4) is the same as the…

A: Solution is done in step 2

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 9ti −…

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Q: dx dt = cos x cos²t

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