Find the area of the surface generated by revolving the curve about the y-axis. y=4-x², 0≤x≤2.

Q: A conical tank has height 3 m and radius 2 m at the base. Water flows in at a rate of 2 m³/min. How…

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Q: e Transform of f(t) = sin²t By Rule.

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Q: Question 1. A critical point of the function g(x, y) = ey + 3x²y-y is (0,0). Use the Second…

A: See this solution in below

Q: [(x+1)e(x²+2x) dx

A: Given :∫x+1ex2+2xdx

Q: x+2y+xy'=0  solve thisODE w/o using the Exactness Method. use another method. what method ?

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Q: 9. Let R be the region bounded by r=1-y²₁ x=2 + y²₁ y=-1, and y = 1. Find the volume of the solid…

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Q: Find the Do not include "f'(x) =" in your answer. derivative of f(x) = (-x³ - 2x² - 2x) sin (x).

A: Given f(x)=(-x3-2x2-2x)sin(x)

Q: (t) below, find f'(x). f(x) = (3x³ + 3x²-4).x²

A: Given a function f(x)=(3x3+3x2-4)x2 Formula used : d(xn)=nxn-1

Q: Question 3. The parametrization of a curve C is given by r(t) (a) Find r' (π/6). = (sin(t), cos(t),…

A: To find parametric equations of the tangent line to the given curve.

Q: The following differential equation (+1)² + 2²/ x2 dy x² has an order of 02 3 01 = sin x

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Q: 6. fx√4x+1dx

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Q: 11) S₁0 x ³ lnx dx

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Q: Compute the double integral ff(6zy2 +12z³y + 4y) dx dy with R= 3,5 z [1,2].

A: See this solution in below.

Q: 3. Evaluate the definite integral (a) (b) (c) (d) 256 15 15 256 Cr 62 f(x+ (x+2)√x+1 dx.

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Q: Consider the following functions. f₁(x) = x₁ F₂(x) = x², f3(x) = 3x - 7x² g(x) = c₁f₁(x) + C₂f₂(x) +…

A: To find whether given functions are linearly dependent or independent.

Q: In problems 1 and 2, list both the order of the DE and state whether the DE is linear of nonlinear.…

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Q: Find the indefinite integral of the following function:

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Q: x² - xy (x,y) (0,0) √√√√y If it exists, find lim Answer: .Write DNE of the limit does not exist.

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Q: Simpson's 3/8 Rule for integration is mainly based upon the idea of O Approximating f(x) by a 3rd…

A: To Find : Idea on which Simpson's 3/8 th rule is based on

Q: Determine p'(x) if p(x) = (5x)7x and x = 4. Select the correct answer below: O 2028 (51n 20) O 20…

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Q: III. Evaluate the given definite integral: ₁*√x edx

A: ∫14 xexdx here we have to integrate using substitute method  so for that lets substitute x = v dv/dx…

Q: Given that F(x) = a) F'(x) bl 5'(4) 2 1 1 + 2 dt.Using the 2nd Fundamental Theorem of Calculus, find

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Q: I can't seem to understand the solution. Can someone write it down?

A: An inner city revitalization zone is a rectangle that is twice as long as it is wide. A diagonal…

Q: Refer to functions m and q. Evaluate (qm) (x) and write the domain in interval notation. Write your…

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Q: Suppose w = x³yz + xy +z+3 and x = 3 cost, y = 3 sint, z = 2t. Then dw dt t= . [Show solution.] =

A: Given :w=x3yz+xy+z+3x=3costy=3sintz=2t

Q: @)X = y² + 1₁ x = 0, y = -1 y = 2 The appropriate integrand to find the volume of the solid…

A: Solution is given below:

Q: The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a…

A: To find velocity at time t  and distance travelled during given time interval.

Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = 4 + xy - x - 2y, D is the…

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Q: * The Simpson's Rule gives the exact result when applied to any polynomial .of degree-➖➖➖➖➖➖➖or less…

A: Simpson's Rule: It is a numerical method for approximating the integral of a function between two…

Q: 6. Find the (xy + 1) dx + x (x + 4y − 2) dy = 0 integrating factor and solve DE. In x + xy + 2y (y −…

A: A detailed solution is given below.

Q: frequent problem in surveying city lots and rural lands adjacent to curves of highways and railways…

A: We have to find the total area of the given picture which contains one right angle triangle and one…

Q: Bernoulli Differential Equation: Find the general solution 2 = x³y4 x dy dx y-³ = cx6 + 3²4 2y-3 =…

A: To solve differential equation

Q: Find the general solution of the following DE. y' = 3 (y + 1) O y = 3ce³x - 1 Oy = ce³x - 1 Oy =…

A: y' = 3(y+1) dy/dx = 3(y+1) dy/3(y+1) = dx dy/(y+1) = 3dx now apply both side integration

Q: Find an equation of the line tangent to the graph of f(x) = (5x − 9)(x + 6) at (2,8). The equation…

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Q: how did you get ln n - ln 2

A: Given sequence  an = (ln3-ln2)+(ln4-ln3)+(ln5-ln4) +.... We observe this series This series going to…

Q: Question 10 of 17 > dh\ dt =2 5 The variable h is the height of the ladder's top at time t, and x is…

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Q: A bus has 8 vacant seats in the first rose. If three additional passengers enter the bus in how many…

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Q: Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is…

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Q: ³ sin y - 3) = √10 ² Let f(x, y) dt 1 + cos² (t) 16 Then f (2, π/6)=

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Q: A Nathan organized pile X of paper on his desk, and Gerald organized pile Y on his desk. The figure…

A: Volume is just the amount of space contained within a 3-dimensional object.

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

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Q: Find the area of the region bounded by y = 6-x-x² and the x-axis 125 6 (a) A = square units 6 (b) A=…

A: The given curves are; y=6-x-x2 and x-axis or y=0.   Now find the x-intercept of the the curve…

Q: Ex3. Find the absolute maximum and the absolute minimum values of the function f(x, y) = 2 + 2x + 4y…

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Q: III. Partial Fraction Decomposition: Evaluate the following integrals using partial fraction…

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Q: Find the area of the region bounded by the curves, x = −6 ,  x = 6 , the x−axis  and the parabola…

A: Follow the procedure given below.

Q: Find the derivative using logarithmic differentiation. r³(2x - 1) (5x + 1)7(x + 1) 14. y=

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Q: T² T³ T Y pln(y+z) e dxdzdy = [Show your solution.]

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Q: 18. Two cars start moving from the same point. One travels south at 60 mi/h and the other travels…

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Q: Using the two points (x,y) and (x₁,51) to find Lagrange interpolating polynomial, L.(x1) is always…

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Q: Given that f(z) = (z+ 2)(z²z+4) Find f(1 - 2i)

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