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Q: 1-10 J = exp(-x²)dx 0 Evaluate J by means of Simpson's rule with n = 2m = 10 and h = 0.1

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Q: Prove that d/dx(cos x) = −sin⁡ x using the definition of the derivative.

A: Given: fx=cosx   As we know from the definition of the derivative; The expression for the derivative…

Q: Evaluate the limits using the L'Hopital's lim (tan x) (sin x-1) x+2+

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Q: Find the area in square units bounded by the following: (Show graph and detailed solution. Box final…

A: Here, the area bounded by the curves: y=x3+1 and x-axis  with the limits x=0 and x=3 is:

Q: In spherical coordinates, the integral •√√4-x²-y² IMM x² /4-22 None of these. 2π *π/2 2 S √²* [*¹²*…

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Q: Evaluate f(x³ - x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

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Q: Find fx (x,y) and f, (x,y). Then, find fx(1, -2) and fy (-3,3). f(x,y) = -2xy +9y² + 10 fx(x,y)=

A: We can find the answer as below.

Q: quickly

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Q: (y² - x² sin xy) dy+ (cos xy - xy sin xy + e²x) dx = 0

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Q: S 36x2+25 - dx

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Q: What is the integral of (2 sec^2x - sinx) dx? * O 2 cosx+tanx + C 2 tanx + sinx + C 2 tanx + cosx+C…

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Q: find the symmetric equation of the line through point (1,-2,-4) which is orthogonal to the plane…

A: We have to find the symmetric equation of the line through point (1,-2,-4) which is orthogonal to…

Q: Nxx X-√√x 3 olx

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Q: Question 1 Express the Laplace Transform of the following functions: (a) f(t) = 2t sin(3t) - 3te5t…

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Q: Solve the following matrix equation for a, b, c, and d. a-b b + c |-|8 8 3 88 3d+c 2a - 4d a = b =…

A: We will find the value of a ,b ,c ,d by solving the given matrix equation in the following step.

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: The equation of the curves are: C1: y = x2 ⇒ x = y                 for first quadrantC2: x = y2 To…

Q: What is the y = x^2 - 4 and x-coordinate of the centroid of the plane region bounded by y = 2x - x^2…

A: Here we have to find the x coordinate of the centroid of the area bounded by the curves.

Q: The human population of Earth in July 2014 was 7.295 billion, and was expected to grow by about…

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Q: What is the y-coordinate of the centroid of the plane region bounded by the x-axis and the…

A: Given

Q: T Evaluate sec²20d0 a. 00.33 b. 0.5 c. 0.67 d. 0.25 e. NONE OF THE ABOVE O A OB O O D OE

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Q: Determine whether the improper integral converges or diverges, and find the value if it converges.…

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Q: The curve has an equation of r = 4sin0. Compute the area bounded b the curve. 12.57 11.18 16.89 O

A: Given :r=4sinθ

Q: What is the x-coordinate of the centroid of the plane region bounded by the x-axis and the…

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Q: IV. Solve the following problems completely. 3 1. Use local linear approximation to estimate √(3.…

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Q: II. 3 4. 5- 10² - 0 + (0² + 0) dx S le* -e (e* e) e 0 Evaluate the followin

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Q: The following differential equation is a Bernoulli equation: 2 dy = y³ where y = f(t) dt t By making…

A: To convert into linear differential equation.

Q: Find the volume generated if the area between y = coshx and x- axis from x = 0 to x = 1 is resolved…

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Q: 12. We have the following width measurements of 80 meters wide lake Distance: 0 10 20 30 40 50 60 70…

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Q: lim x→0 sinh x2 – x2 sinhx−x

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Q: 3 2 พ 2 cos2 4x dx

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Q: Find the area of the region bounded by: 21. x + 1 = 0, x-3 = 0, y + 4 = 0 andy-5=0. 22. 2x + 3y = 6,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Perform the integration. π ¹3 sec³ x tan x dx √2 + secx 0

A: A detailed solution is given below.

Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

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Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

A: Here, R'(x)=(x+2)ln(x+2)

Q: What is the y = x^3 and y = x^2? O2/5 3/5 6/35 12/35 y-coordinate of the centroid of the plane…

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Q: What is the center of gravity of the solid formed when the plane region bounded by 2x+y-2= 0, y = 0…

A: Center of gravity is given.

Q: Inventory Microbucks Computer Company makes two computers, the Pomegranate II and the Pomegranate…

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Q: Given that R' (t) = 2ti — 2j + 3t² k and R(2) = i + j — k, then R(t) =

A: The objective is to find R(t).

Q: What is the y=x^2 - 4 and O 1/2 -1/2 3/2 -3/2 ONA y-coordinate of the centroid of the plane region…

A: Let's find y co-ordinate of the centroid of the plane bounded by two curves.

Q: Given that -3 9+x² following functions: (-1)n+1 32n+1 4x (9+x²)² Σn=0 2. g(x) = x2n. Obtain the…

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Q: Find the area of the surface generated by revolving about the x-axis the ellipse x = acost, y =…

A: We need to find area. NOTE - As per Bartleby's guidelines we can solve one question from multiple…

Q: Find the derivative of the function. s = t In |t| ds dt 11

A: The objective is to find the derivative.

Q: II. Evaluate the following integrals. 2. (sin³x)√1 + cos x dx KIN k 플

A: Here is the solution:

Q: Jill burns 100 calories per hour while sleeping, 300 calories per hour while walking, and 200…

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Q: Perform the integration. 3 [² (13² - 11 + 13* - 31) dx

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Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

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Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

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Q: Why is it =10πr33? particularly, why is the value 33?

A: Let's solve.

Q: P(x, y) = 10x + 6.1y-0.007x² -0.035² where x is the number of pounds of Kisses and y is the number…

A: ∂P/∂y is the derivative of P with respect to y taking x as a constant..

Q: 4 fcos 3x sin³ 3x dx

A: