I. Evaluate the following limits 2. lim (3 + x)² x → +∞0

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

A: Given

Q: 4.) Give the general solution of the following ODE: x" + 3x - 4x = 0.

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Q: 8. Find the area of the region in the first quadrant bounded by the curves y = sin x, y = cos x and…

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Q: Sketch and set up integrals for volume of the region bounded by y = x^2 + x - 2 and y = 3x + 13…

A: Please see the below pictures for detailed solution.

Q: -2 Given f(x) = ²√4 - t² dt, evaluate the following. -2 (i) f (-1) (ii) f(0), by interpreting f (0)…

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Q: What is the the x-axis and the semicircle y = (4 - x^2)^1/2? 00 O 1 02 04 ONA x-coordinate of the…

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

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

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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: Kindly write this, I cant understand by text

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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: u=-5), v=-1-√31 (a) Find u-v. U-V= (b) Find the angle between u and v to the nearest deg 0

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Q: 3. +∞ 8 -∞ dx x² + 1

A: Given ∫-∞∞dxx2+1To evaluate the integral:

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1-7x)y², y(0) = 6…

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Q: 3 4-3x S²³ So dx dy

A: To evaluate the given double integral.∫03∫04-3x dx dy

Q: Find the area bounded by the curve y = coshx and the x-axis from x = 0 to x = 1. a. 11.75 sq. units…

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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: The total cost of producing 1 unit of a product is given by C(x, y) = 80+ 0.3x² + 50y - xy dollars…

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Q: Your farm encompasses 900 acres, and you are planning to grow soybeans, corn, and wheat in the…

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: Use the linear approximation to estimate In (√0.99).

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Q: 5(-6)+(-4)(-1)/2^2-3+(-1)

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Q: Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: The position of the sun at sunset, north or south of due west, depends on the latitude and the day…

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Q: Stan 3x sec 3x dx 3.

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Q: 10x-3y For the function f(x,y,z)= 8z + 1 fx=0 find fx. fy. fz, and fyz-

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Q: Find the 4th midpoint Riemann sums of function f(x) = x³ +3 on (0,2) Blank 1 with respect to a…

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Q: 3 2 พ 2 cos2 4x dx

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Q: The weekly investment report shows each company's stocks with its high bid, low bid, closing bid…

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Q: Find the general and the particular solution: d²u du = 4(1 + 3v)²; u = -1,and = -2 when v = -1 dv²…

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Q: velocity function of a particle moving along a horizontal line is given by v(t) = t² = 6t + 8, re t≥…

A: Please refer to the image below

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

A: The given region is as follows: Now, rotation of the bounded region about y-axis will result in a…

Q: Determine the order of the given differential equation and state whether the equation is linear or…

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2, y = 1, and…

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Q: I. Determine the convergence of each of the following series using the indicated test. In number 4,…

A: The given series   ∑n=1∞(-1)nn+3

Q: Find the area of the surface generated by removing about the x-axis the upper half of the ellipse…

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Q: Find the surface area generated b rotating the portion of the parabolic arc x = y^2 from x = 0 and x…

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Q: 6. csch x dx

A: To find the integral of the given function.

Q: Let f(x, y) = (x³ − x)(y² – 1). Find fry(x, y).

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Q: Using the Ring or Washer method, what will be the equation of the volume of the solid formed when…

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Q: 2 -2 eydo عام 2 + +2

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Q: Find the equation of the plane containing the points (0, 1, 3), (2, 2, 2) and (3, 2, 1)

A: Given: points (0,1,3), (2,2,2), (3,2,1) Find: equation of the plane containing given points

Q: lim (tanx) (sin x-1) x→ 17/1272 π +

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Q: Find fx (x,y) and fy(x,y). Then, find fx(-1,-4) and fy (-3,2). 32 f(x,y) = 4x³y² fx(x,y) =

A: We have to find partial derivatives of Given function.

Q: Find the area bounded by the curve y = coshx and the x- axis from x = 0 to x = 1. a. 11.75 sq. units…

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Q: Remember, even if you enter an answer rounded to a set number of decimal places, if you use that…

A: Explained below

Q: Evaluate the multiple integral.* 22y [ ✓²)¢ dx dy 10 17.5 16.5 The area hounded by the graphs of y=

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Q: Is that pi (π)? Or something?

A: Given ,  Area of the region bounded by  y = cosx , x = -π/2 and x = π/2 and the x - axis  We have to…

Q: 7. Find the area bounded by the curve y = 4x - x^2 and the lines x = 0 and y = 4.

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