dy 1) dx y-x 2) y+x

Q: 5 8. Let f(x) =-x + 4 cos 3x. On the interval 0 < x< 2n, what is the average height of the function?…

A: A detailed solution is given below

Q: /) Set up end eveluete fue defnite integrel for fue ared of tme Surfece fonmed by revoiving tme…

A: The graph y=x2, 2≤x≤8 revolving about x-axis

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. p…

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Q: A particle is moving in a straight line according to the position function s(t) = t° – 6t2 +9t + 5,…

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Q: A certain rumor spreads through a community at the rate = 3y(1+y) , where y is the portion of the…

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Q: Solve the Laplace Transform of the equation f(t)= te⁻³ᵗcos²2t

A: We have to find the laplace transform of the given function.   f(t)= te⁻³ᵗcos²2t

Q: 0.09 ) 12t At the end of t years, the future value of an investment of $37,500 in an account that…

A:

Q: 2. The volume of the sun is 1.4 x 10 cubic kilometers and the volume of the earth is 1.1 x 102 cubic…

A: Earth mass

Q: Evaluate x2 lim За - 10 - x→-2 x + 2

A:

Q: Find the dimensions of a rectangle with a maximum perimeter that can be inscribed in the ellipse 4x…

A: Given ellipse 4x2+9y2=36                -&gt;Equation(1)Let (x,y) be the upper right corner of the…

Q: Exercises: Find the derivatives of: 1. 1-y = (secx + tanx)(secx- tanx) 2- y = x2.cotx- x2 4. 1+cscx…

A:

Q: y"ーy=

A: Given problem:- Solve the following differential equation y'' -y=xe-x

Q: What is the second derivative of f(x) 2x-3 2 x+1 10 (x+1)* 10 3 (x+1)° -10x+10 (x+1)* 10x-10 (x+1)*

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Q: Describe the domain and range of the function. KX, y) = 9x2 - y

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Q: 2. Find an equation of the plane containing the point P(0, –,÷) and the line determined by the two…

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Q: -2x 3. lim, 0 sinx

A: This is a problem related to limit of the function. Based on the general formula and concepts we…

Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8xy? = 2y6 +…

A: We need to find the surface integral.

Q: Find the area between the loops of the limacon r= 7(1+2 cos 0). Area =

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Q: -6 Evaluate , (2x + V) dx. A. 27 + 2/3 + 4/6 B. 27 2/3 C. 27 23 4V6 D. 27 + 4v6

A: The objective of the question is evaluate the definite integral and choose the correct option . Here…

Q: Evaluate the following limit: x + 2 lim x→-3¯ x² -+ 2x – 3 O +∞ 10

A: The given limit,        limx→3-x+2x2+2x-3

Q: d dri(t) • r2(t)] = d [ri(t) × r2(t)] dt ||

A:

Q: 8 3. y2 = x and y² = 2 – x (Answer: S. U. ) 3 - -

A: Given: y2=x and y2=2-x   Now find the point of intersection between the given curves. y2=x,…

Q: S) Ffnd the nolyme of the Solid generatedd by revoluing the region boundeed by the graphs of the…

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Find the exact arc length of the curve x = + 2) ? from y = 1 to y = 5. Enter the exact answer. L =

A: Given problem:-

Q: Evaluate the improper iterated integral. x2 dy dx 1 + y?

A: The solution is given in the next step.

Q: 2) Find and of the following equation then simplify whenever possible. dx x = 1+ Sin t y = Cos? t

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Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the…

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Q: Part A) approximate the area under h(x)=x^2 from x=0 to x=2 using four rectangles and a left…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 sts 1. (y – x) dx +…

A: A detailed solution is given below

Q: Verify Green's Theorem by evaluating both integrals ÔN I y? dx + x2 dy = dA ay ax 'R for the given…

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Q: What is the differential equation whose solution represents the family y = Ae3x + Be4x+Cxe4x? O…

A: Given problem:- Find the differential equation whose solution represents the family y=Ae3x +Be-4x…

Q: 1. Find the derivative of the following. f(x)=13x* -7x²+5x²+11x+75 a.

A: Formulas:ddx(a f(x))=a ddxf(x)ddx(xn)=an xn-1ddx(a)=0;  where a is a…

Q: Use the graph of the function f(x) shown below to evaluate lim f(x). x 3+ 3 2 3 O 3 O 1 O DNE 2.

A:

Q: E1 Fnd all of the Porst order partial derivatives Toll wing fanctions. a)そ= x+5y x Sin (y). b) fexy,…

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Q: 2 2. Find an equation of the plane containing the point P(0, -) and the line determined by the two…

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Q: 5. Which of the following is equivalent to (v2/2 – iv2/2) ? O -2 O 1 O -1/2 O -1 O 2 O 1/2

A: We have to find the equivalent of given complex number.

Q: Use Riemann Sums to calculate the area under the curve over the interval (1,3] for f(x) = x² + 2

A: By using Reimann Sums to calculate the area under the curve over the interval 1, 3 for fx=x2+2.

Q: Find the first three nonzero terms in Maclaurin Series for each function

A: This is a problem related to series expansion. based on the general formula of maclaurin series we…

Q: f(r) = Va +4 – 2 Complete the following table and use it to approximate lim f(r) (Round to six…

A: The given function is: fx=xx+4-2   So, at x=-0.1 f-0.1=-0.1-0.1+4-2=3.974841 At x=-0.01…

Q: Sketch the region R and evaluate the iterated integral | Rx, y) dA. 2x + 8y) dy dx y y y y 2.0 2.0-…

A: Given problem:-

Q: Find the standard form of the equation of an ellipse with the given characteristics. Major axis…

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Q: k S = (d – 2)? where c and k are positive constants which depend on the quantity of smoke each stack…

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Q: 8* – 2* 10. lim, »0 4x

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Q: EVALUATE. 2022 a) x n (xl dx dx 2x+3x+7 dx (x+1) (x² +S)

A: This question can be solved by applying the concepts of indefinite integrals.

Q: You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into…

A: Linear equations

Q: Evaluate the integral using the following values. x dx = 60 x dx = 6, dx = 2 J2 %3D 5x dx J2

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Q: What is the equation of the tangent plane normal to x2 + y2 + z = 9 at the point (1, 2, 4)? O 2x -…

A: Given; f(x,y,z)=x^2+y^2+z-9  Point (1,2,4)

Q: answer is partialy Answer the questions for the following polar equation. 3 r = 1- cose (a) Identify…

A: Parabola

Q: Matching Type. Match the functions in Column A with their corresponding derivatives in Column B.…

A: