Consider the function f(x) = 3x² - 10x +9, 0≤x≤7.

Q: Find the indicated trapezoid approximations to the following integral. 18 [9x² 9x dx using n = 2, 4,…

A: Consider the given information.

Q: Evaluate the following integral, (9x - y²)dx + xy dy where C is given by x X = 5t, y = √t, 0 ≤ t s…

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Q: Solve the following non-homogeneous differential equations: x" (t) + x(t) = 2 cost 1) -X 2) y"+2y+y…

A: The given differential equation is; x2y''-2xy'+2y=xlnx

Q: 2. Isolatex. For answer, show this structure <x< -5 ≤ 2-x < 5

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Q: 2. Set up iterated integrals for both orders of integration. Then evaluate the double integral using…

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Q: For a standard normal distribution, find: P(-1.29 Z-1.07)

A: The given probability .The aim is to find the value of the probability using the standard normal…

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The equation of the curve is given byTo determine: The slope of the tangent line to the given curve…

Q: 7. u = (2, 2), v = (2, −2) 8. u = (2,-2), v = (−2, 2)

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Q: Estimate f (5.06) for f as in the figure. y=f(x)/ ƒ (5.06) ≈ (4,2) (10,4) Tangent line X (Give your…

A: The figure is given as,Estimate

Q: A) Find the derivative of f(g(x)) at x=2  if f(2)=6, g(2)=3, f'(2)=1 and g'(2)= -2

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Q: 10 P.M. an oil tanker traveling west in the ocean at 15 kilometers per hour passes the same spot as…

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Q: If f(x) = f'(x) = f'(4) = tan x - 5 sec x 3x² tan(x) sec(x) X

A: The Quotient Rule:Use the common derivatives:

Q: Let (a) (b) (√x + ²) dr + (y² + ln(2x)) dy=0, x>0. Check that this is an exact differential…

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Q: Find the derivative b. y= sec^-1(2x+1) c. y=x^e^x

A: I have appended the formula used in the solution procedure.

Q: Find aw/as and aw/ât using the appropriate Chain Rule. Values Function w = y³ - 2x²y x = es, y =et S…

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Q: If y = cos² 3x, then =? dy dx dy dx O dy dx dy dx = 6 cos 3x = = -2 cos 3x -6 sin(3x) cos(3x)

A: Given,

Q: 23-28 (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and…

A: (a) To find the intervals on which f is increasing or decreasing, we need to analyze the derivative…

Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 5x² + y² = 4. √20 maximum value…

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Q: Differentiate the function. 1 (5x+172 y =

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Q: HOMOGENEOUS DIFFERENTIAL EQUATION Solve the following differential equations using HOMOGENEOUS DE.…

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Q: 4. Three large tanks contain brine, as shown in the figure below. pure water 4 gal/min A 300 gal B…

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Q: Consider two functions y₁ = f(x) and y₂ = g(x), and that y₁ ‡ y2 except where they intersect. If…

A: Given that two functions  and  and  except what they intersect.These functions intersect at…

Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 5x² + y² = 4. maximum value:…

A: To find the maximum and minimum values of f(x,y)=xy on the ellipse 5x^2+y^2=4, you can use the…

Q: Find f. f(x) = f"(x) = 8x³ + 5, f(1) = 6, f'(1) = 2

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Q: Write the equation 52 = 25 in logarithmic form.

A: Write the equation  in logarithmic form.

Q: Let A(x) = f(t)dt, with f(x) shown in the graph below. 4 3 2 1 X -1 -2 -3 -4 -5 A 5 At what x values…

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Q: Evaluate the definite integral by interpreting it in terms of areas. 7 (3x - 18)dx 3

A: To evaluate the following definite integral by interpreting  in terms of areas.

Q: Use the graph to find the following limits and function value. a. lim f(x) X→2 b. lim f(x) X→2* c.…

A: In this question, we will find the limit by using the graph.

Q: If 1800 square centimeters of material is available to make a box with a square base and an open…

A: Let the side of the square base = x cmLet height of box = y cm

Q: Find the lines that are tangent to the curve y = 2tan(pi*x/4) at x=1

A: The equation of tangent line passes through point  with slope

Q: Determine if the series diverges. If it does diverge, type a upper case D as your answer, and if the…

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Q: e,f,g

A: By using previous solution sign Table xf'(x)Positive zeroNegativeDNENegativezeroPositive

Q: Find the interval containing x = 0 where f(x) = 81x - tan(x) is increasing. Write your answer as an…

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Q: In 2011 a country's federal receipts (money taken in) totaled $2.46 trillion. In 2013, total federal…

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Q: Does the series below converge or diverge? If it converges, find its sum. Either way, justify your…

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Q: b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at…

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Q: Given that (fog)(x)=x-8, which are correct rules for f(x) and g(x) that result in this composite…

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Q: 5. Find the outward flux of the field F = xzi+yzj+k across the surface of the portion of the sphere…

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Q: Consider the graph of distances from the origin as a function of time for a car trip. 150 100 50…

A: This all the given problem by using the concept  slope of tangents at a point.

Q: Question 3 (a) Find and sketch the domain of the function f(x,y)=√x-1+√y-4 (b) Evaluate the limit…

A: Domain: Domain of a function f(x,y) is the set of values of ordered pair (x,y) such that f(x,y) is…

Q: Seperate the variable and solve the equation 2y (dy/dx) + 2x = 0. Use the initial condition x = 0;…

A: The given equation .The aim is to find the solution with the initial value .

Q: In 1994, the moose population in a park was measured to be 4460. By 1997, the population was…

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Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

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Q: 0 -3 5 1 0 1 0 6-58 0 -1 -1 3 4 -2 0

A: The given determinant is

Q: 1. Using the fundamental theorem of calculus part 1, along with properties of the definite integral…

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Q: 2) Find the solution of the given initial value problem in explicit form. Plot the graph of the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01 cm/min.…

A: Radius = 60cmdr/dt = 0.01 cm/min.

Q: Let g(x) = 2x² - 216x. Find the relative maximum and minimum values of g. Also find the intervals on…

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Q: 2. Consider the floor function [.] whose output is the largest integer less than or equal to the…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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