Determine the area bounded by f(x)=x²-x and x-axis. A unit² ® unit² Ⓒunit² 1 D unit²

Q: y = e ²₁ y = 1, x = 2; about y = 2

A: the solve volume

Q: * Integral use to solve if series converges or diverges, give example if true or false

A: It is true that the integral is used to solve if the series converges or diverges. The method is…

Q: Which of the following is NOT a method for finding volume of solids of revolution? A) washer method…

A: Conic method

Q: 8. y = log x-1 x+1

A: Let's find second derivative of given function.

Q: What is the slope of the line passing through the points M (m,O) and N (n.0) with m #n? O 1 Oo m-n…

A: slope=? M(m,0) and N(n,0) M(x1,y1) and N(x2,y2)

Q: Let R be the region bounded by the functions f(x) = -4x² - x and g(x) = -5x as shown in the diagram…

A: This question can be solved using the concept of area bounded by two curves.

Q: 9. f(x) = (2x5-2x+2)/(x²-3)5

A:

Q: Assume that the situation can be expressed as a linear cost function. Find the cost function. Fixed…

A: fix cost $200 20 item cost $400 here per item cost = 400/20 = $20 cost function  C(x) = 200 + 20x…

Q: 11. Determine whether the lines L₁ given by x=t, y = 1+ 2t, z = 2 + 3t, (with x < t < oo) and L₂…

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Q: 3. (D2 + 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

A:

Q: Find the solution of y" − 8y' + 16y = 0, y(0) = 1 and y'(0) = 5. y(t) = Ae4t + Be-4t y(t) = e4t+te4t…

A: The given equation is;  y''-8y'+16y=0, y(0)=1 and y'(0)=5.

Q: J (u-2) (u+3) du

A:

Q: The region is bounded by y = x² - 9 and y = x + 3, find the area.

A: Solve the following

Q: 1.30 Find the value of the integral ₁00 √x dx by using simpson method (n = 6)? 1.00

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Q: Find the value of x If f'(3) = 52? X 1 2 4 f(x) -2 8 X

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Q: What is the range of the function y = 5 sin(0+ 60°) - 4? O -60° ≤ y ≤ 60° O-9≤ y ≤ 1 O-4≤ y ≤9 O-1 ≤…

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Q: Use of an Auxiliary Variable Solve the equation. The sum of two positive numbers is 2. Find the…

A: see below the calculation

Q: Find the slope of the line if it is defined. Through (6,10) and (6,-3) Select the correct choice…

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Q: Evaluate the limit : lim √x+1-2 X-3 x²-9

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Q: ~ f ² f (x) dx = -5 and Given than (A) None of the given choices B) √ f (x) dx = 8 © [²] f (x) dx +…

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Q: f(x) = 4x² 8x +3 - x²+x-12

A: The given function is f(x)=4x2-8x+3x2+x-12

Q: f(x) = Jax+b (2x²-1 if x < 2 if2 ≤ x

A:

Q: 3) x² + y² + 16x+10y+80= 0

A: Given

Q: Find the general solution of the given system. dx - 2x + 3y dt dy dt - 6x + 5y Ex(t), y(t)) 0

A:

Q: 腰 √√/XX S₁ Solve the integral: A 3√√√x² + C √√x² (B) + C 6 Ⓒ6√√x +C dx

A: ∫x3x2dxRewrite:=∫1x56dx

Q: y = tan e³x + etan3x

A: (tan x)' = sec2(x) (eax)' = a eax.

Q: 0 ✓1+13xdx

A: Given that ∫021+13x3dxSolution:let 1+13x=t313dx=3t2dtdx=3t213dtat x=0,t=1at…

Q: Solve the following deferential equations e-2√x y dx b) √x dy =

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Q: Hint: Use polar ca

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Q: Find Maclaurin series for the following functions Ans. Σ 2) 5 sin(-x) Ans. (-5x)" n! 5(-1)"(-x)2+1…

A: The given function is 5sin(-x). Repost the next question.

Q: A box with a square base and open top must have a volume of 171500 cm³. We wish to find the…

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Q: Suppose that cote = c and What does sin equal in terms of c? O sin = √1+c² O 1 sin = √1-c² O sin =…

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Q: Find the area enclosed by r² = 4 sin 20.

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Q: f(x): = Opción 1 5x² - 8x + 15 3x² + 6x 12 y Opción 3 || సా || I 5/3 3 5 Opción 2 Y Y Opción 4 ||…

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Q: Give the domain and range. Then, use the graph to find (a) f(-2), (b) f(0), (c) f (9) 1 (2) Ay Q 40…

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Q: b)show that: I(cosh at cos at) = 5²440*

A: This is a problem related to laplase transform. Here we will use convolution theorem for evaluating…

Q: Use Lagrange multipliers to find the critical points and the relative extrema. f(x,y,z) = x² + y² +…

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Q: Answer and give the complete solution. A 6-ft tall man is walking away from a 15-ft post at a rate…

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Q: Let R be the region bounded by the functions f(x) = 4x² + 6x and g(x) = -2x² - 6x as shown in the…

A: Given f(x)=4x2+6x, g(x)=2x2-6x Here point  intersection of f(x) and g(x) is x=-2 and x=0 Therefore…

Q: d If g(x) = - S* [e'− ln(2t+1)]dt, find g''(x) dx -2 2 A ex. (2x + 1)² 4 (В B et + (2x + 1)² Ⓒe*…

A: Given that gx=ddx∫-2xet-ln2t+1dt

Q: y = 5 tan x³ + sec(3x)

A:

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 [*1/2 cos²0de A 0 Ⓡ IS!" B 18…

A:

Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vfl(-12,-2)=i+j+k (Type integers or simplified…

A: Given

Q: 3. Use appropriate differentiation techniques to determine the first derivatives of the following…

A: see below the answer and calculation

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 5x - 4x²…

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Q: Test the convergence of the following series. (a) Σ*, 1 (b) Σπ=1 2 (c) Σπι (d) Σ*-11+n=

A: We have to check convergency of given series

Q: For the given cost function C(z) = 250√ + find 8000 a) The Justion loval 1000 TUNING b) T. duction…

A: For the given cost function Cx=250x+x28000, to find d The production level that will minimize the…

Q: Find the value of x If f'(3) = 52? 1 2 4 f(x) -2 8 X

A:

Q: Find the area bounded by : f(x)=e*, g(x)=e* and x = 3. (A) (e³-1)² e3 sq. units B (e³+ 1)2 e3 (C)…

A: To find the area bounded by curves

Q: Determine the graph of g = x^2 + sqrt of (x + 1) and solve for its extrema, concavity, and points of…

A: Please see the below picture for detailed solution.