Sketch the region enclosed by x +y 2 and x +y = 0. a) Favoring convenience, should you integrate with respect to z or y? b) What are the limits of integration? lower limit and upper limit

Q: ii) Evaluate the vector line integral of F, F. ds, where y is an oriented curve defined as follows:…

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Q: 4.) Evaluate: xe* dx

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

Q: For The following data, the best fit line is: X 2 Y 12 10 12 3 r will be - 0.987 r will be positive…

A: Explanation of the answer is as follows

Q: (1) Which equation could represent the circle that has the center at A = (-2, 3) and a point B = (6,…

A: Equation of circle centered at (a, b) is (x-a) ^2+(y-b) ^2=r^2 Where r is radius

Q: A sphere with radius 1 m has temperature 16°C. It lies inside a concentric sphere with radius 2 m…

A: answer is in next step

Q: Find solutions of the following equations by the method of separation of variables: 4. 2+= 0 at xe,…

A: 5.

Q: ind the slope of the tangent line to the curve y = V4x – 3 at the point (13, 7).

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Q: Suppose f is a f(8(x))=2x² and differentiable function where 2x f'(x)=2+ f (x). Show that g'(x)=…

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Q: Find the function F that satisfies the following differential equations and initial conditions.…

A: We will find the function.

Q: 8. Find the dimensions of the largest-volume cylinder that can be inscribed in a sphere of radius 10…

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Q: Consider the series an where n=1 (-Зп — 9)2n (-5n – 9)" an = In this problem you must attempt to use…

A: Solve the following

Q: Evaluate the following integral. cos x dx -6x 1 sin 2x dx 2 - 6n O C. dx + cos 2x dx OD. dx + - 6x 6…

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Q: M The diagram shows the curve y = (x+ 1)e* and its maximum point M. (1) Find the x-coordinate of M.…

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Q: Find tan 0. N39 A) tan 0 = 539 8/39 B) tan 0= 39 C) tan 0 D) tan 0 = 39 5/8

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Q: Tell if the piece-wise function is continuous on the given interval. Put a CHECK MARK AFTER the…

A: Given graph,

Q: What is the radius of an expanding circle at the moment when the rate of change of its area is…

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Q: Q21 - In simpson's 1/3rule the intervals must be b) odd c) non of them 3 [2 13 -61 A=2, 2= -2 b) =2,…

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Q: 8) A rectangular storage container with a square base is to have a volume of 2250 inches cubed. The…

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Q: Let u = (3,-2), v = (-2,5), and w = (0,1). Express 10u-4v+w in the form (a,b). 10u-4v+ w= (Simplify…

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: Recall:  L=∫abr(θ)2+r'(θ)2dθ We have, r=7sinθ+2cosθ, a=0, b=π

Q: Which series helps us to derive the discretized form of the governing equations? a. Taylor series b.…

A: (a) Taylor series expansion is normally used to discretise governing equations.

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 - 3t) %3D Find the…

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Q: Perform a first derivative test on the function f(x) = x/25 - x;(-5,5]. a. Locate the critical…

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Q: Find the radius of convergence, R, of the series. (-1)" 2" n = 1 Find the interval, I, of…

A: for radius of convergence of a series  we will calculatelimn→∞an+1an<1  for the series ∑an  and…

Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

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Q: that F(x) = f(t) dt, where V6 +u f(t) = du. и

A: We have to find out solution

Q: Find the indefinite integral. Hint: Let u = 3 - Vx. (Remember the constant of integration. Remember…

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Q: In calm waters, the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that…

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Q: a/3 Find the value of cos(3x) dx.

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Q: Ing light is located 10 feet from a wall. The light completes one rotation every 3 seconds. Find the…

A: From the given data: Here, the complete 2π rotation is done in 3 seconds.  So, dθdt=2π3 rad/sec

Q: Given a = 2t – Int and y = t² – In t, find the following. A) Determine the derivative in terms of t,…

A: Explained below

Q: 2. If f(2, u) dA 10, where D is the triangle with vertices (0, 0), (2,0), and (2, 3), then the…

A: To find the average value of the given double integral.

Q: 2 dx 6) dx sec x csc x 7) -4tan x dx 8) -cot x dx

A: 1. ∫2sec(x)dxWe know that 1sec(x)=cos(x)=2∫cos(x)We know that ∫cos(x)=sin(x)=2sin(x)+C 2. ∫5csc…

Q: Given r = e-, find the following. A Determine the derivative in terms of 0. Show each step and…

A: First we find dy/dx

Q: 3. Find two elevation angles that will enable a shell, fired from ground level with a muzzle speed…

A: Solution: here we use the range formula

Q: compete Mž uing Values ा. ड 2 12 64 X010.5 511o5

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Q: Evaluate the definite integral. (Assume a > 0.) 'al/5 x°Va? - x10 dx

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Q: 2. A bushfire spreads with burning area according to the following function, A(t) = 160t – 40t² (in…

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Q: Find the gradient of the curve y = x° – x2 – 8x – 2 at the point on - - - the curve whose…

A: As we know that; The expression for the gradient or slope; m=dydx And The Power law; ddxxn=nxn-1

Q: Solve the equation (x^4 + 2y)dx - xdy = 0

A: I am attaching image so that you understand each and every step.

Q: Solve the equation y' = csc(x) - y cot(x).

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Q: 1. The position of a particle is given by the function s(t) = t* – 32t where t is measured in…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +4 1' lim t00 9t2 + 10' 8t. |(?,?)

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Q: 12. Solve the second-Order differential equation: d²y - y = e* (use method of variation of…

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Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

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Q: Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: Evaluate y dx+3xy dy, where C is the boundary of the semiannual region D in the upper half-plane…

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Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: a a If f is an even function, why is f(x) dx = 2 f(x) dx? Choose the correct answer below. O A. a a…

A: Definite integration property

Q: Find the indefinite integral. (Remember the constant of integration. Remember to use absolute values…

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