Ex3. Find the absolute maximum and the absolute minimum values of the function f(x, y) = 2 + 2x + 4y = x² - y² on the closed triangle region R with vertices (0, 0), (0,9) and (9,0).

Q: Let f(x, y) = ln(x + y − 1). The domain of f is {(x, y)| x + y > }.

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Q: Find the absolute extremum within the specified domain. 21) Minimum of f(x)=(x2+4)2/3; [-2,2]

A: According to our policies we are allowed to solve one question at a time. Kindly repost other…

Q: Find the area bounded by r = cos 0 for -π/2 ≤ 0≤π/2. 2. Find the length of the r(t)= , 1 ≤t≤ 5 .…

A: We have to solve Questions 12.

Q: Use the graph of f(x) to determine the following limits. The domain of f(x) is x E R. If the limit…

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Q: Write an equation for a rational function with: Vertical asymptotes at x = 3 and x = -4 x intercepts…

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Q: A region bounded by f(x) 6 5 4 3 Find the volume of the solid formed by revolving the region about…

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Q: 1. The radioactive isotope hydrogen-3 has a half-life of 12.3 years. a. If a sample of 80 mg of…

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Q: ƒ(s) = 4s - 18 9-s² What function f(t) has Laplace transform: 5s (s - 2)² +

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Q: 1. Evaluate the definite integral *2³²√³+1 dr. (a) ² (27+2√2) (b) (27-2√2) (c)(2√2-27) (d)/(2√2+27)

A: I have stated the used formula in the solution.

Q: B: Solve the following integrations: fx³e-2x¹ dx b-S. -dx x³ +10 c-f 3sec³x. tanx dx arks

A: a) ∫x3e-2x4dx Let x4=t Then, 4x3dx=dtOr, x3dx=dt4 By substitution,…

Q: a-limx-4(2)

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Q: Find the orthogonal projection of b = [4 2 -4] onto the column space of the matrix A. (Enter each…

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Q: The base of a three-dimensional figure is bound by the line X = √y on the interval [1, 4]. Vertical…

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Q: prove the following properties of the laplace transform, knowing that L{f(t)} = f(s)

A: Prooof of the above properties of laplace is given by

Q: Find the net signed area of ƒ (x) = x - 2 over the interval [0, 6], illustrated in the following…

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Q: (b) Use L'Hopital's Rule to find the following limits: e-1 x (i) limx→0 (ii). lim-0 x-y fl (x > 0, y…

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Q: 12. Integral x² dx x³ +4

A: Given the integral,        ∫x2 dxx3+4

Q: Find the solution of the initial value problem y" — 2y' – 3y = 6te²t, y(0) = 1, y′(0) = 0. NOTE:…

A: We have to solve the given differential equation.

Q: 13. Integral √x dx

A: Here we have to find the integral.

Q: 73. an = (2n + 2)! (2n-1)!

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Q: The figure shows a region in the complex plane. Write an algebraic description of the shaded region.…

A: We have that the center is 4+i. So, we have the LHS as |z-4-i|. We see that (7, 0) is on the curve.…

Q: 5. Find three 2 x 2 nonzero matrices A, B and C such that B C and AB = AC = 0.

A: To find the matrices A, B and C satisfying the given conditions.

Q: Find the largest product the positive numbers x, y, and z can have if x² + y + z = 4. The product is…

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Q: The position in feet of a race car along a straight track after t seconds is given by s(t) = 4t² - t…

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Q: Which of the sequences {a} in Exercises 31-100 converge, which diverge? Find the limit of each…

A: For the given sequence, If limit of the sequence at n -> infinity finitely exist, then we'll say…

Q: Use the formula for the area of a trapezoid to evaluate √₂² (2x- 2 (2x + 3) dx.

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Q: limg-0 2x sinx 4-4cosx

A: We can find the limit as below, using L'Hospital rule.

Q: Let R be the region in the first quadrant bounded by the y-axis, the x-axis, the graph of y = ez,…

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Q: Solve the given differential equation. 16x2y" + 16xy' - y = 0 C₁ cos(In(x)). + C₂sin (In(x)) 4 4…

A: here we have to solve differential equation.

Q: 2) A: By using partial method solve [2x² cos x dx

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Q: In a circumference of radius r (in meters), its radius increases at a rate of 2.8 meters per hour.…

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Q: 1. (a) Write the following set of equations in matrix form. 8=6X3+ 2X2 2-X₁=X3 5X₂+2X₁ = 13 (b)…

A: Here we have to write the equations in matrix form and then we have to do matrix multiplication.

Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

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Q: A bus has 8 vacant seats in the first rows. If 3 additional passengers enter the bus, in how many…

A: For the number of ways of their seating, we need to use combination.

Q: Find the area of the segment of a sphere formed by revolving the graph of y = √25-x2,0 sxs 4, about…

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Q: Write an equation for the function graphed below. The y intercept is at (0,0.2) y = 5 -4 -3 2 -- 1 4…

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Q: Express 3p 12pq+4q² -1- 8p² 6p² +2pq as a single fraction in its simplest form.

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Q: Use the matrices below to perform the indicated operation if possible. 6 B-[-3.0-[1] C [89] -4 = If…

A: Performing the indicated matrix operation

Q: 4: Find the indefinite integral of f(u) = -1-3√ =

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Q: 1. If f is a function, then limf(x, y) = f(2,5). (z,y) →(2,5) 2. If lim f(x, y) = 0, then lim f(x,0)…

A: Answer 1. False

Q: 9. y = logs (e cos(2x))

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Q: +[ƒ Given that 5 ≤ f(x) ≤ 6 for -4 ≤ x ≤7, use property 8 of Section 5.2 of the Stewart Essential…

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Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(1, 1) =

A: The given function is;  f(x,y)=ln(x+y-1).

Q: If f: R → R is a function such that f'(4) = f'(8) = 0 and f"(x) = 18x - 108 so, f(m) is a local…

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Q: Show that there are no tangents to the curve f(x) = 6x3 + 2x2 that have a slope of -5.   Please…

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Q: (1) f(x) = sin (5x + 6) (3) f(x) = sin(x-³) (2) f(x) = sin (3x4 + 2) (4) f(x) = cos (4+ 3x)

A: To find f'(x)

Q: 1215 + 1² + t³ - tdt

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Q: Q4\A: Find area of zone bounded by curves y = x² y = 2x+8

A: area bounded by curve  y = x2  y = 2x +8  step 1  find the intersecting point of curves step 2  find…

Q: Find the area between f(x)=x² - 16 and the x-axis from x = 0 to x = 7. The area is square units.…

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Q: A region bounded by f(x) = x², y = 0, and x = 4 is shown below. 2 Find the volume of the solid…

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