2.8 Find the particular solutions of a) y - x- = 1 + x² dy 2 dy = dx b) (1 + x²)2 dy dx dy dx dy c) y cos²x = tan x + 2, dx d) x(x + 1)- dx' + xy² = 0, = y(y + 1), y = 3/2 when x = 1 y → ∞o as x→ 0 y = 2 when x = π/4. y(1) = 2

Q: 6. Find the value of √2-x² √2-1² (x² + y²) dy dx + [ [ ²* (x² + y²) dy dz 1- √√2J-√√2-1² by…

A: given integral I =∫-2-1∫-2-x22-x2(x2+y2)dy dx + ∫-11∫x2-x2(x2+y2)dy dx now cosider I = I1+I2 Where…

Q: Use the method of variation of parameters to determine the general solution of the given…

A: Given differential equation is y4  +2y'' +y = 3 sint Take ft = 3 sint  then y4  +2y'' +y = ft

Q: 2 3 3 4 + 5 7 Divergent Conditionally convergent Absolutely convergent None of these Other: 5 9 + :

A:

Q: A train is required to run between two stations 1.5 km apart at a schedule speed of 36 km/h. The…

A: Given information Distance  between two stations D= 1.5 km Schedule speed  of train Vs = 36 km/h…

Q: Determine the 1st and 2nd degree Taylor polynomials L(x, y) and Q(x, y) for ƒ(x, y) = e¯x²-y²…

A: Given function is fx,y=e−x2−y2cosxy. We have to determine the first and second degree Taylor…

Q: Expand the given function in a Laurent series valid for the indicated annular domain. (Give all…

A: Laurent Series : It is a power series expansion for a function. If the function f(z) is analytic…

Q: Evaluate the improper intergal 1 5x - dx using the residue (x² + 16) ³ 3 theorem.

A:

Q: 56. How many seating arrangements are possible for 5 people to sit in the 5 seats of a car if 1…

A:

Q: Given

A: We solve by Gaussian Elimination method.

Q: 8 Find the circumference of the circle pictured above. Round your answer to the nearest hundredth.

A:

Q: Determine the 1st and 2nd degree Taylor polynomials L(x, y) and Q(x, y) for f(x, y) = e¯¹²-y²…

A: Consider the function fx,y=e−x2−y2cosxy. The first degree Taylor polynomial Lx,y for the given…

Q: the point (2.1). (1.12, 1.25) O(1.19,1.42) (1.17, 1.37) tes

A: The given parabola is y=x2 Let the coordinates of the point be (x,y) The distance   between  the…

Q: Expand f(z) = f(z) = Z (z+1)(z-4) 0</z+1|<5 in a Laurent series valid for the indicated annular…

A:

Q: 1) Let T: R³ → M2×2 (R) be a linear map and suppose the dual map has matrix (with respect to the…

A: As per the question we are given the dual transform T* from M2×2(R) to R3 in matrix form, and a…

Q: 100 8. The nth partial sum of the series = 1 an is given by Sn Find the 5th term using the sum.…

A:

Q: Give the definition of supremum and infimum for a nonempty subset of R. 2. Provide some examples to…

A:

Q: (2) Show that Jo for a > 0 but not for a = 0. lim 818 √ne-na² da a lim √ne-na2 748 da

A: We have to show that,   limn→∞∫α∞ne-nx2dx = ∫α∞limn→∞ne-nx2dx  for α&gt;0  but not for α=0.

Q: A random sample of 600 students from Delhi University are selected and asked their opinion ab out…

A: Here we use χ2-test for test hypothesis. Formula( χ2-test for Independence of attributes) :…

Q: 2.11 Let A = p cosa, + pz² sin o a (a) Transform A into rectangular coordinates and calculate its…

A: Given A=ρcosθaρ+ρz2sinθaz

Q: • f (x,y) = x ³ cscx + secy√ sinx cot y * finel fx, fxx, fy fyy fyx fxy

A: Given function is fx,y=x3cscx+secysinxcoty. We have to find the partial derivatives of the the…

Q: Find the numerical aperture theta if the MN=8 cm, PR=8cm and the distance from the tip of the…

A: Given that MN=8 cm, PR=8 cm and the distance from the tip of the connector to the surface is d=6 cm.…

Q: Find the approximate area of ​​the part of the plane x=z that is between the planes y = 0 and y = 6…

A: As per the question we have to calculate the area of the plane surface x = z bounded by the planes y…

Q: A DIGITAL CHIP MADE BY YOUR MICROELECTRONICS DIVISION, COUNTS CONTINUOUSLY IN THE SEQUENCE: IC 2048,…

A: The sequence is 1024,2048,4096, 8192,... The common ratio is 20481024=2,40962048=2 Therefore the…

Q: (b) Calculate f(z) dz. (c) Why did we show that the right hand limits at 0 = 0 of the real and…

A: Let us start solving the problem step by step

Q: 4 Determine whether the series Σ converges or diverges. If it converges, find its sum. 7m m = 2…

A:

Q: Here is the route that Laura and Jean-François take on a hike up a mountain trail to a small…

A: The route that Laura and Jean-Francois take on a hike up on a mountain trail to a small cottage and…

Q: let theorem a, beR such that acb. Use the axioms and that : about prove a) Find R to b) Find CEIN:…

A:

Q: 3x +2y-z = 3 +7z=9 + 5z = 12 (2x-3y

A:

Q: Expand the given function in a Maclaurin series. f(z) 1 (1 +9z)² M8 ( k = 1 R= = Give the radius of…

A:

Q: Find the general solution of the following differential equation. 4y" + 20y' + 25y = 0 NOTE: Use c₁…

A:

Q: Find the F.T. of the fall wing Signals (functions) * (t) = 1 + cos (6π t + T )

A:

Q: 2) Let V₁, V2, W be vector spaces over F. Show that the set Bil(V₁ × V₂, W) of bilinear maps is a…

A:

Q: 3. Write the integral that gives the area of the surface generated when the curve y = sin x + 2, for…

A:

Q: 7. Set up an iterated double integral equal to the mass of the lamina in the shape of the region…

A:

Q: Find the general solution of the following equation valid near the origin: (1+4x²) y¹¹-8y=0…

A: Given: Let us consider the given differential equation, 1+4x2yιι-8y=0

Q: α Ση = 2 3 V n 4 3 4n - 2 + 5

A:

Q: Prove if it is a group or not. 1. G = {x ER | 0<x< 1},x*y= xy 1-x-y+2xy 2. G={TERIO<r<1} r * U = U

A: Now we discuss the four properties needed to prove it is a group.  Closure:  since…

Q: Find the critical numbers of the function f(x) = 12x5 - 75x4 - 100x³ - 5 and classify them. At x =…

A:

Q: Find the mass and center of mass of the thin constant-density plata shown i the pure to the right…

A:

Q: 2. An airplane is flying towards a radar station at constant height of 6 km above the ground. If the…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: solve y''-y'=xex using variation of parameter . Do not use any formula

A: using variation of parameter . First we find the solution for homogeneous equation. From that…

Q: a = 268 b = 752 e. Prove that if g = gcd(a, b) then gcd (2) = = 1

A: Given that a = 268 = 2 × 2 × 67 b = 752 = 2 × 2 × 2 × 2 × 47   Now let g = gcd (a, b) = gcd ( 268,…

Q: Show that the set of all rational numbers is not complete

A:

Q: BE THE LINEAR TRANSFORMATIONT: R³ P3(R), GIVEN BY T(x, y, z) = (x + y) + (y −z)t + (x + z)t² +…

A: Given: The linear transformation, T:ℝ3→P3ℝ given by Tx,y,z=x+y+y-zt+x+zt2+y-x+zt3. The matrix…

Q: Determine the 1st and 2nd degree Taylor polynomials L(x, y) and Q(x, y) for f(x, y) = е-¹²-y²…

A: A multi-variable function f(x,y) is a rule that associates or fixes a number to the particular point…

Q: Consider the initial value problem (1 + x + 2x²)y" + (1 + 7x)y' + 2y =0, x>0, y(0) -1, y'(0) = -2.…

A: We have to  (a) Show that x = 0 as an ordinary or singular point. (b) We have to find the first five…

Q: Determine whether the following series converges. Justify your answer. 9 k+4 Σ| cos k=1 COS 9 k+5…

A: Given the series  ∑k=1∞cos9k+4-cos9k+5

Q: Determine whether the series ខណៈ 4-1 5" n=0 D. Select the correct choice below and, if necessary,…

A: I have given the answer in the next step. Hope you understand that

Q: Task 7 is done by Select an answer Task 8 is done by Select an answer starting at time starting at…

A: From the given system we have to find the processor and starting time of a particular task.

Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: By Trapezoidal rule we have ∫abf(x) dx≈h2f(x0)+2f(x1)+2f(x2)+2f(x3)+f(x4)h=b-an=1--(1)4=12Evaluating…