Find an appropriate change of variables (and then use it) to evaluate 1/₁₂ (x + y)² ex²-y² dx dy R where R is the square with vertices (1, 0), (0, 1), (-1,0) and (0, -1).

Q: Estimate the area under the graph of f(x) = x² + 4x + 1 over the interval [ – 3, 0] using five…

A: Here we have given a functionf(x)=x2+4x+1. Now plotting the graph of the given function we get.

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A: Concept: Trapezoidal rule : ∫ydx= h2[y0+y6+2(y1+y2+y3+y4+y5)] Simpsons one-third rule: ∫ydx=…

Q: Solve the differential equation. sec(0) Be de dt

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Q: (1) Use the Limit Comparison Test to determine if the series is convergent. η3 1 Σ+2 n=3 .

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Q: (a) (b) x + y f(x, y) = √√x+y f(x, y) = sin (x+y) √√²-1

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Q: Find the extreme values of the function and where they occur. y=x²-3x² +7x-10 The maximum is 6 at x…

A: Given query is to find the extreme values of the function.

Q: Find the average temperature in the box D = {(x,y,z): 0≤x≤ In 4, 0≤ y ≤ In 8, 0≤z≤ In 16) with a…

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Q: Let Ġ(x, y) = (x², y). Calculate the flux of G across the line segment from (0, 0) to (1, − 2).

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Q: Consider the following. 62 1 + ex (a) Find the exact solution of the exponential equation in terms…

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Q: Determine the type of conic section that each general equation will produce. a.)x²+y²+8-4y-2=0…

A: To determine the type of conic section.

Q: Find the​ equation(s) of the tangent​ line(s) to the graph of the indicated equation at the​…

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Q: (a) A water container, whose circular cross section is 6 ft in diameter and whose height is 8 ft, is…

A: Given:    A = area of the tank a = area of bottom hole…

Q: A water tank in the shape of an inverted circular cone has a base radius of 2 m and height of 3 m.…

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Q: Determine the values of λ for which the system below has nontrivial solutions. (5-2)x-5y=0…

A: The given equations are; (5-lamda)x-5y=0 -3x+(3-lamda)y=0

Q: A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r…

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Q: Consider the following. 300 (1.025) 5 = 1100 (a) Find the exact solution of the exponential equation…

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Q: The demand function for Wally Winka's Neverending Lollipops is given by p= (12-x)In(x + 7) where p…

A: Given  p=12-x lnx+7 is the demand function When x=6    p6=12-6 ln6+7           =6 ln13   Rate of…

Q: Initially an 800 gallon tank contains 400 gallons of water in which is dissolved 50 lbs of salt.…

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Q: The following function is continuous at x = 0. f(x) = ex, { 9x² + x + 1, x < 0 x≥0

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Q: f(b)-f(a) Find the value or values of c that satisfy the equation b-a f(x) = 3x³ - 3x², [-1,2] =…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. tan(x) y =…

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Q: eah expressi 36 Si=1/3180° < 0 <3·10° 0 ter 0 312=80 Simplify 3

A: Given that:sinϕ=-13 ;           180°&lt;ϕ&lt;270°

Q: Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. 1. Find the gradient of f(x,…

A: The given function is; f(x,y,z)=x2yz-xyz3.

Q: 21. lim 8118 2x5 - x x² + 3

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Q: (c) f(x, y, z) = ln(x+y+z)+√√√x+y+z x+y+z xyz

A: As per bartleby guidelines we only give first question answer. Please repost for other parts.

Q: 2. In each item, give the standard equation of the circle satisfying the given conditions. a. center…

A: as per the rules we are supposed to answer only the first question and rest other can be reposted.

Q: x) = (x-10) ¹

A: Given query is to find the critical points.

Q: and flux of F=(x, 7T T ≤t≤ the circulation y) on C: r(t) = (3 cos (t), 3 sin(t)) for is positive,…

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Q: Use Laplace transforms to solve the initial value problem: y" - 10y' +9y = 5t, y(0) = -1, y'(0) = 2

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Q: 3t² + t 3 t→→∞ t³ - 4t + 1 11. lim r - p³ r→∞ 2 - r² + 3r³ 13. lim

A: see below the answer and explanation

Q: Find f′(x) and simplify.   f(x)=6x5 (x 4 − 2)  F'(x)=.......?

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Q: 1) Consider the function f(x): = 5x² - 4x +7 Find a number c in the domain such that f (c) = defined…

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Q: The function f(x) = 2x³ - 45x² + 300x + 9 has one local minimum and one local maximum. Use a graph…

A: Topic - Local extrema's of a function We are given an equation, f(x)=2x3-45x2+300x+9And it's known…

Q: Problem 1. 1 (a) 100 2²2² + +9 dx Explain why each of the following integrals is improper. 4 1 (b) ²…

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Q: 1. Use the limit comparison test to determine whether the infinite series is conver a. Σn=27³-1 b.…

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Q: "roblem 9. True or False. Explain your choice carefully. is convergent. nv2, n = 1, 2, 3, ... is…

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Q: 1. Find the derivatives of the following functions: a) f(x) = 2x³ + e²x b) f(x) = ln (2x - 1)5

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Q: 17 Let I = [x² dx = 1596 and consider the Trapezoid Rule, T(n), and the Midpoint Rul 5 a. Compute…

A: Let's find T(12) and M(12).

Q: (²cos(x)) = 2cos(x) — 4xsin(x) – x² cos(x) Otrue O false

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Q: 5. Find the equation of a parabola with vertex at the origin whose properties are given below. a.…

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Q: Consider the sequence. √20, √20+ √20,√√20+ √20+ √20 (a) Compute the first five terms of this…

A: Consider the sequence,20, 20+20, 20+20+20a To compute the first five terms of this sequence.b To…

Q: Find an equation of the tangent line to the curve y=x√x that is parallel to the line y = 3 + 3x. y =

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Q: ʼn object is thrown vertically upward whose height is given by the function s(t) = − 16t² + 35 here t…

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Q: -4-x² - y² 4 component. For the function f(x, y) (-3, -3) that has a positive find a unit tangent…

A: Let's find unit tangent vector.

Q: (b) Hence find the value of | Vy 2y(1 + y2x) ey?x dx dy. (c) Find the value of vaz-x2 ( + )

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Q: Consider the point (음, %) Fort 1. Find (sc (t) A).& 10 22-1 B) 은 C) - 음 이응 Ja 100 0)-10 F) - g) none…

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Q: Why does it make sense to model the monthly temperature with a sine or cosine function? Part 2.…

A: We need to model trigo. function.

Q: Find sin 2x, cos 2x, and tan 2x if sinx = - sin 2x cos2x tan 2x = 11 0 0 2 √13 and X terminates in…

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Q: Find the maximum rate of change of the function f(x, y) 2y I at the point (4,5).

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Q: Given f(x, y) = 4e¹² sin(2y) then ▼ f(0, π) =

A: The objective is to find the gradient of the functionat the given point.