Find an equation of the tangent line to the graph sin(x) + y² = 4 at (π, 2).

Q: find the Fourier series of half rang periodic function. f(x) = x|x| -π < x < π <x<π

A: We know the following. Fourier series of function fx on interval -L≤ x≤ L is defined as:…

Q: 2. The Substitution Method states that A. If F'(x) = f(x), then [ f(u(x))u' (x) dx = F(u(x)) + C B.…

A:

Q: 3 -1 0 2 2 х -у 2 x+y 2 dx dy

A: Given

Q: Differentiate the function. g'(x) = g(x) = 2x² - 8x + 13 gx 8 2 X Read It Need Help? Master It

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Q: I. 4. Evaluate each determinant. 2 -5 2 -1 4

A: We have to find out determinant

Q: 1. Let R be the region in the first quadrant enclosed between the circles x² + y² = 9 and x² + y² =…

A: x= rxos(theta) y= rsin(theta)

Q: 1. Find the area between the curve f(x)=√x and g(x) = x³.

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Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: Given : Let I be a proper ideal of the commutative ring R with identity. Then I is a _______ if and…

Q: Example 1: Evaluate the integral: ₁²²=238+1² 2r-3 - 3x + 1 dx.

A: The given integral is (2x-3) /sqrt(x2-3x+1), limit from 3 to 5.

Q: he table of integrals to evaluate the integral. (Use C for the constant of integration.) sin (20) J…

A: The solution is given below.

Q: 7) y = exz 8) y = 3 x ²

A:

Q: Q4/Find the slope of the line 3x-4y=-8 and then find the distance from the point P(3,-2) to this…

A: Given Equation of line3x-4y=-8To find slope &amp; Distance.

Q: Q1. The parametric equations of the lines L1, and L2 are given as: L: x=-2+1, y=3+2t, z=-t+4 L₂:…

A: Let's find distance between two lines.

Q: Simplify. Write "undefined" for expressions that are undefined. -3 -6 6 1 4 -4

A: Given that a  matrix problem and we do simply these matrix by using general property of matrix.…

Q: For the following function, find the Taylor series centered at x = 5 and then give the first 5…

A:

Q: 2 ³₁²₁²[z³(x + y)³] dz dy dx -4 J

A: In this question we have to solve the given triple integral.

Q: Find the area of the region bounded by the curves 1 y = (x+4)²¹ Y = 4 and the x-axis using vertical…

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Q: Differentiate the function with respect to y. A Z = + Bey уб Z' + Bey = 8A 9 y 20 -

A: In this question we have to differentiate the function with respect to y.

Q: The value of A. +3+2x² +C C. = + x² +2+C 20 [ (² + 3) *²x² dx B. +³²+3x³ + C 28 D. none of the…

A:

Q: Evaluate: (4x²yz - ) dz dy dx

A: Let,    I  =∫23∫-14∫10 (4x2yz - z44) dz dy dx           I = ∫23∫-14[∫10 (4x2yz - z44) dz] dy dxI=…

Q: 2 3) 9 = x ² sin x y વચ્ચે ઝ 4) y = sin x 1-2 cos x

A:

Q: Evaluate √x/2 6sinx(cosx+1) do

A:

Q: The value of A. -√4+C 4x B. +C √4-2 C. D. 4√4-x² 4√4-x² S ₁4- +C +C dx (4- x²)1.5

A:

Q: Evaluate the definite integral. 8 [x√x - 7 dx 5.06

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Q: зи Evaluate the integral: So So So u s2 +u2 ds du dt

A: Given: I=∫02∫0t∫03uus2+u2dsdudt   As we know the common integral. ∫11+x2dx=tan-1x+C

Q: -3 -2 ²₁ ² [z³(x + y)³] dz dy dx

A:

Q: derivative of (√2)^csc4x

A:

Q: Consider the parametric curve: X = sin² (t) y = -9t Which integral gives the arc length of the curve…

A: Topic = Integration

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

A: Let's solve given diffrential equation by using laplace transform.

Q: f(x) = x - 3, g(x) = x² Find (f + g)(x). 2 - (f + g)(x) = x+x-3 Find the domain of (f + g)(x).…

A: It is given that f(x) = x-3 g(x) = x2 We need to find the solution to the given questions.

Q: The value of √x dx 1+ A. x-2√x+2 ln (1+√√x) + C B. x-2√x-2 ln (1 + √√x) + C C. x-2√x+2 ln (1+√√x) -…

A:

Q: A solid is formed in the first octant bounded by the plane z = 6 - x - y and the cylinder 4 - x².…

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Q: 1. Find the Inverse Laplace Transforms of the following. 3s 2), 35544 2

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Q: Find the volume of the solid obtained by rotating about the x-axis the region bounded by the curve 2…

A: The answer is given below:

Q: [*[f(x) + g(x)] a 6 -5 f -2 Y = 7 -3 7 x -6 9 -2 Y 10 5 3 5 2 x

A: We have to find the value of given integration.

Q: Set up but do not evaluate an integral that represents the volume of the solid of revolution 2x + 1…

A: Given:   y = 2x + 1      y = ( x - 1 )2

Q: 4. Evaluate the double integral: To fo (Hint: Change the order of integration to dy dr.) y dx dy.…

A: We have given the double integral in which the region of integration 'R' is given below  R : { 0 ≤ y…

Q: 31² If the velocity function of a moving particle is given by v(t) = 6 – + x, find the position…

A:

Q: • show that (x, y, z) = PDE : 2²4 ахг 824 дуг + 2 x² + y² + z² = 0 8²4 dz² satisfies the

A: This question can be solved using the concept of partial differentiation.

Q: Water is flowing into a conical vessel 18cm deep and having a diameter of 10cm across the top. If…

A: We have to find the rate of volume.

Q: 1. Find the Inverse Laplace Transforms of the following. 3) 3s³+3s s6 3

A:

Q: Use Stokes' Theorem to find the circulation of F = 5y + 5zj+2ak around the triangle obtained by…

A: We have to find the circulation of F→.

Q: Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

A:

Q: (3) If R is an integral domain has non zero characteristic, then Char(R)=..... (i) 5 (ii) 4 (iii)9

A: Option (i)

Q: Evaluate: 3₂₁ [2³(x + y)³] dz dy dx

A: Given: I=∫-23∫-12∫01z3x+y3dzdydx   As we know the Power Rule: ∫ax+bndx=ax+bn+1an+1+C, where a &amp;…

Q: For the following exercises, use the second derivative test to identify any critical points and…

A: Given :f(x,y)=-x2-5y2+10x-30y-62

Q: 6. Evaluate the line integral y²³ dr + ²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: In this question, we need to evaluate the given line integral.  The given vertices of rectangle are…

Q: Solve the given differential equation. All solutions should be found. dy 3x²-8y- y³ 8x + 3xy² dx…

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Q: xy' + (x +1) y xe sin 2x

A:

Q: Evaluate: xy² dx dy S

A: Given: ∫04∫0yxy2dxdy