A function f(x) is given by the table of values. Approximate the area under the curve y=f(x) between x=-4 and x=2 using the Trapezoidal Rule with n=6 subintervals. -4 -3 -2 -1 1 2 f(x) 4 5 3 10 11 2

Q: If m s f(x) s M for a s x s b, where m is the absolute minimum and M is the absolute maximum of f on…

A: We use given property and solve it.

Q: The function f is continuous on the closed interval (0, 6] and has the values given in the table.…

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Q: A function f(x) is given as a table of values. Approximate the area under the curve y=f(x) from x=-4…

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Q: A football is 10.8 inches from tip to tip and 7 inches in diameter at its thickest. The shape of the…

A: Consider f(x)=-0.12x2+35. f(x)=0⇒-0.12x2+3.5=0⇒x2=-3.5-0.12⇒x=3.50.12 ≈±5.4 We find the volume by…

Q: (a) Estimate the area under the graph of f(x) = 6 + 2x from x = -1 to x = 2 using three rectangles…

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Q: hat is the area of the region bounded by the line x = 4 and the curve x³ = x² + 2xy - y² = 0. ht:…

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Q: The function f(x) = x² – 8x + 12 is positive on (0, 2) and (6, 10) and negative on (2, 6). Find the…

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Q: 2. Determine the area of the region bounded by the curve y = x³ - x² - 2x, and a. the x-axis the…

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Q: 3. Consider the function for r +0 f(r) = 1 %3D for r = 0. (b) Divide the interval [-1,1] into 2n…

A: given function is                                            f(x)=1x;  for x≠01 ;  for x=0 we have…

Q: If m s f(x) SM for a s x s b, wherem is the absolute minimum and M is the absolute maximum of f on…

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Q: -Vx b. Find the area bounded by the curve y Vxe- and the x-axis from x = 0 to x = 4.

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Q: Q1/ N Use the Trapezoidal rule to estimate the value of f(x) -2x sin'x in the interval x-0 to X-x…

A: A)f(x) = 2x sin2xfrom x = 0 to x = πwith n = 5Trapezoidal Rule∫ab f(x)dx = ∆x2 (f(xo) + 2f(x1) +…

Q: a)i) Calculate the area of the region enclosed by y=x2 , lines x=1 , x=3 , and the x− axis. Round up…

A: The Given curve is y = x2 The equation of the parabola is  y = x2. The vertex is at (0 , 0 ) and the…

Q: 1. Evaluate Sox2+4* dx 2. Find the area bounded by y = 4x², x = 2 and x = 6. 3. Find the area…

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Q: 6. Using the trapezoidal rule with three ordinates an estimate of the area under the curve y = sinx…

A: As per our guidelines, we are allowed to answer only one question. Since, you have asked multiple…

Q: nsider the following equations. Fy) = y? + 7 glv) - 0 y- -1 y = 2 etch and shade the region bounded…

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Q: 3. Find the absolute maximum and absolute minimum values of the function f(x,y) = x* + y* – 4xy on…

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Q: 1. Use the midpoint rule with n = 6 to estimate the value of the integral (x + x)dx. (5 points) 2.…

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Q: Q4A) Find area bounded by y = 0, y = 1-x²,x= 0 and x = 1. B)Is w=zx¹ analytical function or not? 2 2…

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Q: (a) Suppose f"(x) = 0, what can you say about f (x)? Write it in general form. (b) Find the area of…

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Q: Find the area of the region bounded by the graph of f(x) = sin x and the x-axis on the interval [-…

A: Given: The expression to calculate the area under the curve 'y=f(x)' and the x-axis between x=x1…

Q: If m s f(x) s M for a s xs b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: The area bounded by the parabola y- = 4ax, x- 1, x = 2 is given by axis and the ordinates x = Select…

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Q: Find the area between the curve f(x) = x2 +11 and the x-axis from x = 3 to x = 7. The area is square…

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Q: The function f(x) = x² – 8x + 12 is positive on (0, 2) and (6, 10) and negative on (2, 6). Find the…

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Q: Using the Trapezoidal rule, the approximated value for the integral: g(x) dx, is equal to------ g(1)…

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Q: A) Give f(x)-V-3 find f-*(x) ,x >0 B) : Find the area bounded by the curve y = f(x) =v2x +1 and the…

A: We have to find  A) f-1(x) for f(x) =√(x-3)  B) area bounded by the curve y = √(2x+1) and the lines…

Q: 10+ 8+ f(x) 6- 4- 2 个十 -4 -3 -2 1 2. 3 Approximate the area between f(x) and the x-axis from x = -4…

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Q: Determine the area, in square units, of the region bounded on the right by the line g(x) = -3x+27,…

A: Given thatgx=-3x+27fx =-x-52+16To find: Area bounded by the region with respect to y.Note: right to…

Q: If m M for a < x < b, where m is the absolute minimum and M is the absolute maximum of fon the…

A: The graph of tan 2x is increasing in the interval π/8 to π/6,

Q: The maximum value of the function f (x,y) = x² + 2y² – x in the region x2 + y² < 1 O 3/2 O 9/4 O…

A: The maximum value is 9/4

Q: If m s f(x) s M for a sxs b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: 1. a) Find the area of the region lying between f(x) = x^2 − 3x + 2 and x − axis between x= 2 and x…

A: Therefore here area is given by definite integral   Area = ∫x=2x=4f(x)dx ⇒Area = ∫x=2x=4(x2 - 3x + 2…

Q: 3. Consider the function for x +0 f(x) %3D for r = 0. (b) Divide the interval [-1, 1] into 2n parts.…

A: using trapezoidal rule

Q: Find the radius r and the height h of a cylindrical can closed on both top and bottom that has a…

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Q: f: R\{0} → R, f(x) = +5z-2-1 e

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Q: . Consider the function f(x) = (2 – r) /4r – a2. 1. Sketch the graph of f(x) (skip second derivative…

A: The answer is given below in the next step:

Q: where does the 2 that gets pulled out infront of the integral come from?

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Q: Consider the function g (x) = ±x² +1. What is the approximate volume of a solid that is formed with…

A: GIVEN: g(x) = (1/4) x2 + 1

Q: 7. For the function f(x) = cos x, find the net area of the region between the curve 0, and find the…

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Q: According to the short-term statistics theorem, the wave spectrum graphed below consists of a…

A: x f(x) .5 0 .6 0.0032 .7 0.0598 .8 0.1857 .9 0.2686 1 0.2743 1.1 0.2371 1.3 0.1456…

Q: If m < f(x) < M for a < x < b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: Q4) Find the integral value of the function below by using trapezoidal rule y= x'+x-5 (a=1, b=5,…

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Q: 2. Let k > 0 be a constant. The area bounded by the x-axis, the curve y = 1 and the lines x = 1 and…

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Q: 1. Find the area bounded by the region y = 3x + 1, x=1, x=3 and the x-axis.  a. 8 b. 11 c. 14 d.…

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Q: (a) Given the curve of y=x -x(x+3)(x-2)(x-5) i) Sketch the graph for -4<x<6 ii) Find the area of the…

A: Given curve y=110x(x+3)(x-2)(x-5) First we find point of intersection with X-axis, Therefore put y=0…

Q: 2- A function f (x) is given by the table of values. Approximate the area under the curve y = f (x)…

A: We have to find area under the graph by trapezoid rule.

Q: on Find the absolute minimum and maximum of the function f(x, y) = 2x¹ - xy² + 2y² the region 0≤x≤…

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Q: 1 2 1. Find the area bounded by the curve y =x² + 5, the x-axis, and the vertical lines x = 2 and x…

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Q: 1- x Find the area of the region between the curve y = 2- 0 < x < 1, and the x-axis. p2 1 1'

A: here we have ................x-axis ................given interval