Let C be a nonempty subset of a bounded set D. Why does inf C and sup C exist? Show that (c) inf D ≤ inf C and (d) sup C < sup D.

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Q: Solve the given differential equations: X 2. y' = , y(0) = -2 y+x²y

A: To solve the given differential equation.y'=xy+x2y, y0=-2

Q: ۔ ۔ میرا میرے = 3 422 + 81(1 + 2 )2 dy .dz

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Q: The doubling period of a bacterial population is 10 minutes. At time t = 80 minutes, the bacterial…

A: Given: The doubling period of a bacterial population is 10 minutes. At time t =80 minutes, the…

Q: Evaluate the iterated integral by converting to polar coordinates. 2 *√2x - x² 6²6² 4√ x² + y² dy dx…

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Q: Solve the given initial value problem. x³y² - y³ = 45 ³y² + xy³ = 18 x²y² + xy³ = 90 x¹ y² + y² =…

A: Here we have to solve the differential equation.

Q: Graph the rational function f(x)= ↑y K -12 -10 -6 -4 S -2 12- 10- 8+ 6+ 4 Y 2- -2- 4 -6- -8- -10-…

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Q: Solve the given differential equations: == 3. 3x²y dx - (x³ + y³)dy = 0, y(1) = 2

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Q: Graph the rational function. -2x+2 -x+4 Start by drawing the vertical and horizontal asymptotes.…

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Q: f (Ina) ² da 2

A: This question is based on integration by parts.

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Q: A car sharing service offers a membership plan with a $50 per month fee that includes 10 hours of…

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Q: 7- cos y dx + (x siny-cosy)dy = 0 8- (1+ y²)dx + (2xy + y² + 1)dy=0

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Q: Find the vertical shift of the sinusoidal function. fx -3πT -2T Simplify any fractions. T 6 5 ★ تلا…

A: Concept: The sine function's general form: y=Asin(Bx+C)+D The vertical shift: This is the vertical…

Q: Let S = { 1 − (−¹)ª | n € N}. Determine inf S and sup S. Justify. (-1)" n

A: Given : S=1--1nn|n∈N   To Find : inf S and sup S

Q: 4. Given vectors: ū=(4, 9), v = (-8, 15) and w=(2, 10) b) Write ū as a linear combination of and w.

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Q: Suppose that the marginal revenue from the sale of x units of a product is MR = R'(x) = 3e0.01x.…

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Q: Use Newton's method to approximate a root of the equation 4 sin(x) = x as follows. Let x₁ = 2 be the…

A: answer is in next step

Q: 2. In π 2 π ln - 4 e* cos(ex) dx

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Q: Find the integrating factor by inspection then solve.  y(3xy + 1)dx - xdy = 0

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Q: 3- (2x+y)dx + (x-2y)dy=0

A: If the differential equation is of the form Mdx+Ndy=0 which is exact thenSolution of the…

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Q: Hand written plz 9. Find inverse Laplace: es S

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Q: Verify Property 2 of the definition of a probability density function over the given interval. f(x)…

A: Given problem:- Verify Property 2 of the definition of a probability density function over the given…

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Q: If c = 192, ZA = 79° and LB = 55°, b ; Assume ZA is opposite side a, LB is opposite side b, and ZC…

A: answer is in next step. please give a like !!

Q: For the function f(x) = 2x³-5x² +11x +3, find f''(x). Then find f''(0) and f''(2). To find f''(x),…

A: The given function is f(x)=2x3-5x2+11x+3

Q: Given f(x) = = Domain: 1 x + 2 and g(x) = 6 X - 4' find the domain of f(g(x))

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Q: 1. (a) Find an equation of the tangent plane to the graph of x² + y² + z² = 16 at (0, 2, 2√3).

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Q: Solve the given differential equations: 1. dy x3 dx 2+y²

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A: We have to determine derivative