Problem 11.4. Find all local and global extrema of the following functions in the indicated regions a) f(x, y) = x² + y² - 12x + 16y, for x² + y² ≤ 25

Q: Show that the following equations have at least one solution in the given intervals, b. (x - 2)² -…

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Q: Let a be a real number. Evaluate the following integral: So fx + y dady

A: ∫0a∫y-1y+1 x+ydxdy this is given  find double integration  further step given below

Q: If w = f(r,s,t), r = x-y, s = y - z, t = z − x then aw дw ?x + О O -1 -2 Əw дz 1 2 (

A: It is given that, w=fr,s,t, r=x-y,s=y-z,t=z-x.   The objective is to find the value of…

Q: dy (8) The solution of differential equation: + y = xy³ is dx (a) = x + ²+ce²ª, y (b) = x² + + ce²x,…

A: Using differential equations

Q: Q17 Suppose f(x) Is find f(e). Choose a) 3 b) 1/3 a Solution of your c) 1 d) answer 9 2 y'= (y+3)² x…

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Q: 2. (x² + y² + 1)dx + x(x − 2y)dy = 0

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Q: The following table shows a housing index that can be used to compare housing prices in different…

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Q: 9. using prime factorisation, find the HCF of (i) 2622, 1653 (ii) 1891, 1098 10.Check whether 12"…

A: We have to find out hcf

Q: xy²dy=y³x³y(1)=2 3 3 ху

A: See the answer below

Q: The area enclosed by one petal of the polar curve r = cos20 is False True O

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Q: ABSENT STUDENT The formula A = 1000 x 2 models the population, A, of aphids in a field of potato…

A: Concept: The population is represented by A=1000×2t Here for the present population the value of t=0…

Q: 10. Use the definition of the limit of a sequence to prove that (3n+1 lim 2n + 5/ for all positive…

A: we have to use definition of limit of sequence.

Q: b. The formula A(t) = 19.6e0.0138 models the population, A(t), of a US state in millions, t years…

A: Given: At=19.6e0.0138twhere At denotes the population in a US state in millions, t years afterthe…

Q: If √²₁ √√1-y² x² + y² dxdy is changed to equivalent integral in polar coordinates, then the…

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Q: Let f(x) = xe ⁹x. a. Find the values of x for which the slope of the curve y = f(x) is 0. b. Explain…

A: To find out the values of x for which the slope of curve is 0.

Q: Using Linear Equation, find a general solution of: dy x x - y - 5x4 3x² + 2x = 0 dx

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Q: Eliminate the parameter t to find a Cartesian equation in the form z = f(y) for: [z(t) = 3t² y(t) =…

A: We can express x in terms in terms of y as below.

Q: What does the index value of 78.8 in 1990 mean? Explain your reasoning. Year 1960 1970 1980 1990…

A: Ratio of the gas price index in 1990 to the gas price index in 2000 is 0.788.

Q: 3+2=?

A: What is the value of 3+2

Q: What is the area bounded by the curves y² = 4x and x² = 4y? A. 5.33 C. 8.22 B. 4.33 D. 9.11

A: There are more than 1 questions, as per the Q&A guidelines i am answering the 1st question. If…

Q: Find equation of tangent line y=4x cos x at the point (π, -4π) y = mx + b where M = and b =

A: To find tangent line .

Q: Three different forces act on an object. They are: F₁ = F₂ F3 Find the net force Fact on the…

A: Please refer to the image below

Q: Hos solv the step? ₁0.9062cos (1-√3x) d x [sin (1-√√3x) -√√3 √³x)] -0.1 -0.1 sin (1-√√3a) - sin…

A: We have to solve the step  sin(1-√3a)= -0.9556+0.9210

Q: Let a be a real number. Evaluate the following integral: Sofyx + y dxdy y-1

A: This question is related to double integration, we will solve it using given information.

Q: 1. Find a result by using variable separation 101 b- y³y+x³=0

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Q: f(x) = 2 cos x - cos 2x.

A: Given function f(x) =2 cos x - cos 2 x    ; [0, 2π]

Q: Q31 Find the Laplace Transform to the following function L sin2t cos3t

A: Given: Lsin2tcos3t

Q: I need to solve the integral

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Q: Using Determination of Integrating Factors, solv y' = 2xy - x

A: Given differential equation y'=2xy -x

Q: Given the following information, evaluate the other five functions. sec 0 = cos 0 = sin 0 = tan 0 =…

A: Given the value of secθ and we want to calculate the values of other trigonometric ratios.

Q: Determine the Cartesian equation of the line passing through A(4, -2), which has 7=(5, 3) as its…

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Q: Determine the following limits, using ∞o or - ∞o when appropriate, or state that they do not exist.…

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Q: A projectile is launched straight up in the air. Its height​ (in feet) t seconds after launch is…

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Q: fins the voulme of the solid with cross-sectinal area A(x).   A(x) = x+2. -1 <x<3

A: fins the voulme of the solid with cross-sectinal area A(x).   A(x) = x+2. -1 &lt;x&lt;3

Q: Find the general solution of the given differential equation. x²y + x(x + 2)y = ex y(x) = Give the…

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Q: 7. Tammy is golfing. She wants to drive her ball from the tee to the hole that lies due east.…

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Q: The alternating series En-1 (-1)" is diverge. n³ 2n³+3 True O False

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Q: A-Show if the series is convergent or divergent (2n)! 2n n²

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Q: Use Green's Theorem to evaluate 75 -90 -78.77 Le Fix of 2+9=25

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Q: We want to use the Alternating Series Test to determine if the series: Σ (-1)²+1 k=1 converges or…

A: Given series ∑k=1∞  (-1)2k+1 k3k7+17

Q: Evaluate the following integral using change of coordinates: SR S x³ + xy² dedy where R is the…

A: Solution given below

Q: 2π 1. The region R is bounded by the x-axis, x = 0, x = 3 A. Find the area of R. sin(). 2 and y =…

A: Given: Region R is bounded by x-axis, x=0,x=2π3 andy=3sinx2

Q: 1.5(8x³ − 6x² + 12x - - 9)dx

A: Using the formula of integration x^n

Q: Given cost and price​ (demand) functions C(q)=110q+45,000 and p(q)=−2.1q+860​, what is the maximum…

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Q: The particular solution (yp) of the equation y" - 3y' + 2y = 5 e* is yp = -5xex False True O

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Q: 1. Which of the following is incorrect? a. b. [(f(x) · g(x)) dx = [ f(x) dx . [ g(x) dx [(f(x) +…

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Q: d²y (x) dx² 6 dy (x) + By(x) = xe ²x xẻ dx / general solution ?

A: We have to find the solution of differential equation

Q: The population of a city is 89​,000. If the population grows continuously by 3.2​% per​ year, in how…

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Q: d the exact length of the curve. =√y (y - 3), (y - 3), 4 ≤ y ≤ 16

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Q: Find equation of langent line y=-6-2x-3x² at (1,-11)

A: To find the tangent line.