If u = x¹y + y²z³, where x = rse, y = rs²e-t and z = r²s sint, find the value of Ou/Os and Əu/ər when r = 2, s = 1,t = 0.

Q: 8+2x-x² x-4 8 x=4 than f(x) is continuous at x = 4. book Ask my instructor I T - |0| √i 5 Vi 1, 3…

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Q: A plane is defined by the equation x - 7y - 18z = 0. a. What is a normal vector to this plane? b.…

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Q: 7. Evaluate the integral

A: answer is in next step.

Q: Find dy dx 1. 2 y = coth(esinx) tan-1(oooh x3)

A: As per bartleby guidelines we only give first question answers.

Q: 2 ind the arc length for f(x) = 6-2 x² over the interval [0, 2].

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Q: Explain what it means to say that lim_ f(x) = 4 and lim f(x) = 6. X-2- x → 2+ O As x approaches 2…

A: We have to explain limit

Q: 2. Determine the centroid of the area bounded by the curves y = 4x + 16, x = -2x = 5 and x-axis.

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Q: question

A: We have to choose the correct option from the given options according to the given information

Q: 3 S₁ x ³ exdx

A: Evaluate the definite integral :        ∫01x3exdx

Q: In how many ways can a team of 5 people be formed from a group of 5 Germans, 3 French, and 4…

A: Such prolems can be solved by using permutation .formula used in permutation is:-Prn=n!(n-r)!where…

Q: Let R be the region enclosed by the curves y = x³ and y = 2x² The area of R using horizontal element…

A: The area of the region R enclosed by the curves, y=x3 and y=2x2 is given by Area=∫cdg(y)dy

Q: 2 S²₁ (x² x) dx ,

A: To find out the integration.

Q: For items 1-2, identify the substitution equations and solve the solution for each. (x - 2y + 5) dx…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Let's solve given diffrential equation.

Q: A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the…

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Q: Calculate ∞0 1 e -3t √t - dt

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Q: 2 Find the volume of the parallelepiped whose edges are represented by |A=i-13j+4k, B = 31+2j-7k and…

A: Given.

Q: 2 0 ¹³² [², [²³² ²² dz dy da. SIL Question 2. Evaluate the following integral

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Q: Find ay dx 3. 4. 5. y = 2e³x5tanhx y = xln(5x-2) y = sec ¹(log 7x)

A: Given :y=2e3x5tanhx4. y=xln(5x-2)5.  y=sec-1log7x

Q: Define the following sets: A=(1,3,7,9,10) 6-(2.5.7.8.9.10) C = (0,1.3.10) D=(2,4,6,8,10) E=xxis a…

A: Natural numbers do not include negative numbers.

Q: | a 0.24) tan(sin-1x) = b) c) =x d) 1 - x2 3

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Q: 2. Evaluate the double integrals by iteration. whre B is the region 0 ≤ x ≤ 1, ² ≤ y ≤ = d.A

A: Let's evaluate given double integral.

Q: (b) Which one of the following differential equations can be solved using the substitution approach?…

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Q: Solve the general solution of the equations in items 3-4. 2 (2x² + y²) dx - xydy = 0 C Oy-1=x-3+C…

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Q: (b) Find the general solution of: = yx² - xy ax Given z = y when x=1, determine the particular…

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Q: Let f(x) = 8x²(x-2) + 15. Find the critical points c that correspond to local minima. (Use symbolic…

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Q: Q5] Find Maclaurin's series f(x) = ev²x.

A: Follow the procedure given below.

Q: ute the area of the polygon with vertices at 5,1), (3,-10), (-3,-3) (-2,0)

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Q: Q3/ solve the differential equation below: 1. 2-3x+2y=0 (Complementary Function) k

A: The given differential equation,       d2ydx2-3dydx+2y=0

Q: Differential Equation d²y dx² 1) d³ y dy dx3 dx 2) (D³ + 3D² 4D - 12) y 3) 2D4 +11D³ + 18D² + 4D 8 =…

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Q: 1.ſv 2x - x² dx

A: Let's solve given integral.

Q: Given the differential equation xy³dx + (x²y² + 1) dy = 0, What is SN ? dx

A:

Q: The height of a sand dune (in centimeters) is represented by f(t) = 850 - 2t² cm, where t is…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral…

A: We have to approximate the given integral.

Q: 1. 2y" — 7y" + 12y' + 8y = 0

A: Note:- As per your request i am solving here question no. 1

Q: Let R be the region enclosed by the curves y = x³ and y = 2x². If we revolve R about the line y =…

A: The equation of the curves are given by C1: y = x3C2: y = 2x2 The volume of the solid generated by…

Q: Evaluate the integral. √3/2 x² V1-x² dx

A:

Q: Find an equation for the tangent line to the graph of the given function at (-5,29). f(x)=x² +4 Find…

A: f(x)=x^2+4   (-5,29) slope=m=dy/dx m=dy/dx=d(x^2+4)dx=2x m=2x (-5,29) m=2(-5)=-10

Q: - Find the mass of a lamina bounded by y = 5√7, z = 1, and y o(z,y) = x+2 0 with the density…

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Q: 1. Find the value of (0) for a solution (x) to the initial value problem: 6y" + y' — 2y = 0; y(1) =…

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Q: 12. Find the area of the triangle bounded by the lines y=x+3, y=2x-1 and y=-3x+4

A: Solution: Given lines, y= x +3.....i y= 2x-1.....ii y= -3x+4.....iii By using intersection points of…

Q: Let R be the region enclosed by the curves y = x³ and y = 2x². If we revolve R about the line y =…

A: Above question is solved.

Q: Find the area under the curve y = 3x 2 from = 1 to x = 2 .

A: We have to find the area of the given curve.

Q: 2. 2 y² - 4y + 10 dy

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Q: Find the nth Maclaurin polynomial for the function. 4x - 5 f(x) n = 4 x + 1 P4(x) = =

A: The function is  f(x)=4x-5x+1

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

A: We have to find the interval of convergence

Q: Evaluate the given indefinite integral. 7 c 7 cos √6x dx= [ (Type an exact answer. Type an…

A: Solution: ∫7cos 6xdx Apply integration by parts

Q: Find dy dx 4. y = xln(5x-2)

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Q: Write the equation to represent the distance of the rider from the vertical axis after t seconds?

A: