(x²y + 2xy² – y³)dr – (2y³ – xy² + =*)dy = 0.

Q: Given that x=t3+t and y=3/2t4+t2, find dy/dx, d2y/dx2, d3y/dx3

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Q: %3D /Q5) Find volume of body bounded by z2 +y2 + x2 = 4.

A: To find the volume of the body bounded by z2+y2+x2=4.

Q: QI) Evaluate the integral dx dy using polar coordinate

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Q: cos x sin'x dx can be evaluated by factoring sin'x as (sin?x)²sinx and transform sin?x into 1– cos²x…

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Q: Question 18 Consider Evaluate O (9x4+6x)e (x3+y2) O (3x²+6x)e «³+y?) O (6x²+ 3x)e «³+y?) O (6r*+9x)e…

A: Topic = Derivative

Q: Substitute x = 120 and y = 160 in s = x + y. (Only positive values need to be considered.) %3D 2. +…

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Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of does the curve has a…

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Q: g"(x) sin(x- 1) x-1 -4 13 A(x) = kr -8x + 6, -1 10 x>3 8 3 -1 (E) Find all x value(s) on the open…

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Q: Q3) Evaluate triple integral y(x2 -y?)dz dx dy.

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Q: Q3) Evaluate triple integral f, L(x - y?)dz dy dx.

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Q: Q2) Solve the D.E dy – (2x/1- y²)dx = 0

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Q: Please answer the question below: Explain in detail which test you are using to determine…

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Q: The limit represents a derivative f' (a). Determine f(x) and a. 14h lim 1 h→0 (Express numbers in…

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Q: Matrix Operations [2 1 3 3 If A = and B = find: 0 1 2 2 -1 6. ЗА - 2В 8. -5 (A + 2B) 7. А+2(В — A)

A: The given matrices,   A=2-13012 and B=-13-12-11

Q: r= sin E-0) in first quarter.

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Q: Q4) Find plane area inside the polar function r = 2sin E-0) and outside T= sin in-e) in first…

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Q: Since f'(c) f(1) – (0) f(1) – f(0) = 1, f(c) = 1. We therefore equate f'(x) to 1 and solve for x.…

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Q: Find the speed at the given value of t: r(t) = (e4, -9,4t-1),t = 4

A: We know that V(t)=r'(t)Here r(t)=<et-4,-9,4t-1>Differentiate…

Q: 1. Water is being poured at the rate of 2 n m³/min. into an inverted conical tank that is 12-meter…

A: The water is leaking at the rate of π/2 m³/min.

Q: Find y' if 4 cos x cos y = 3y. %3D

A: To find the derivative.

Q: Approximate the critical numbers of the function shown in the graph. Determine whether the function…

A: Explained below

Q: Differentiate the following function and factor fully. g(x) = (2x – 1)*(2 – 3x)“ |

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Q: Given Ax) = - 2 use the first principles definition to find f'(1).

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Q: Evaluate: / sech[in cosr Janx dx A -2 tan-1(e cosx) +c cOsx B) None 2 tan -(e cOx) + C COSA D - 2…

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Q: Find the Area bounded by the curves y² = x and x = 2y – y². %3D

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Q: Find the centroid of the region bounded by the parabola y= 8x and the line y=2x. O (0.8,2) O (1,4) O…

A: We need to find centroid of the region.

Q: u+v+w=0ad u =3, v=5, w = 7 then he angle between y and y is 0 2r 6. 0 5m ONone of the choices 11

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Q: Ob.2 amom +C Evaluate +Vrdx Oa.5 2 5 3 2 Oc 2 wn +C Od 3 +C 2/3

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Q: 1 dt. o t4 +5 Let f(x) = Find the derivative f'(x). e2x none of the choices et

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Q: Q3) Evaluate triple integral f , (x2 -y²)dz dx dy.

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Q: 3. The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

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Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: inside polar functionr = 2 and outside p in third auartor

A: We have to find the area according to the given information

Q: Is Rolle's theorem valid for the function f(x) = Vi-x on the segment [-1,1]? a. No since the…

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Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of , does the curve has…

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Q: Q2) Solve the D.E x²dy + (3xy- 1)dx 0 %3D

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Q: wolloi or oisuleu 6. (-3x+15x") dx 12x 15 12 dx 7. + 3 x'

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Q: Evaluate f Vr+ V?dx Oa. 3 am +2) +C (V2) +C can) Ob. 2 am +2) +C 30 om +C (25) Oc 2 an +m) +C O d. 5

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Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at æ = for f(x) = cos(x). %3D T2(x) must…

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Q: 2 3) -2

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Q: 1 Find "(x) if Ax) -. %3D X+1. 1 (x+1) (x+ 1) -2 (x+ 1)3 12

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Q: Given the triangle 30 find the length of side x using the Law of Sines. Round your /36° 17° final…

A: Given,            The triangle is shown below :

Q: (a) P, : 6x – 3y – 7z – 2 = 0 P2: - 36x + 18y + 42z – 5 = (0 O Parallel O Perpendicular O Neither…

A: topic - vectors

Q: Calculate the derivative by expanding or simplifying the function. 1 – 2(19t) s(t) = (19t)1/2 (Use…

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Q: Consider the series 0 n=1 2+n3 For what values of p does it converge? I. p> 1/2 II. p< 2 O l only O…

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Q: Find the derivative of f(x)= (Inx Oa 6x(Inx Ob. 4 inx Oc 12(in a Od 24(inx

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Q: : / yº sech(e™mv) tanh (» ) dy 7lny Evaluate: @ -ch(7) + C None

A: Given problem:- ∫ y6 sech(e7ln(y)) tanh(e7ln(y)) dy

Q: Find the absolute extrema of the function on the closed interval. h(s) = [0, 2] S-3 minimum (s, h) =…

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Q: A particle is moving in space and its position at time t is given by r(t) 4(cos t)i+ 4(sin t)j+ /²k,…

A: Given problem:-

Q: (a) Show that the integral test applies, and use the integral test to determine whether the series…

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