Tính diện tích phần mặt của mặt nón ~ = Diện tích mặt cho bởi công thức S = D√√²+2+1dA trong đó và y Hình chiếu D của mặt S lên mặt phẳng Oxy có biểu diễn trong tọa độ cực D = {(r, 0): 0₁ ≤ 0 ≤ 0₂, r₁ ≤ r ≤r₂} với 0₁ và 71 Suy ra diện tích mặt cho bởi: 0₂ 72 So, ² √ (r, 0rdrdo S : 6V22 + y2 nằm giữa hai mặt phẳng ~ =0 và ~=5 trong đó f(r, 0)= Vì vậy S= 0₂= 72

Q: Consider the nonhomogeneous differential equation: -2y+y=(E). Given that 3-e' and y, xe are two…

A: The differential equation is y''-2y'+y=exx. The linearly independent solutions are: y1=ex and…

Q: 28 Use the Integral Test to determine if the series shown below converges or diverges. Be sure to…

A:

Q: Find the solution of with y(0) = 2 and y/(0) = 5. y = y" + 4y = 96 sin(4t) + 96 cos(4t)

A:

Q: i. Using an appropriate known series or otherwise, state the Maclaurin series for the function f(x)…

A: We know Maclurin's Series for  (1+x)n=1+nx+12nn-1x2+16n(n-1)(n-2)x3+..... Lets use it to find the…

Q: 1 s²-8s+25] 2) L-1 L- laplace

A:

Q: Check the convergence of the following power series, find the radius and interval of conver- gence:…

A: Given: a ∑1∞nnxn b ∑1∞ x+πnn c ∑0∞x2+13n To find : Radius and interval of convergence

Q: Exercise: 5 a) Find the outward flux of the vector field F(x, y, z) = x³i+y³j + (z³ + xz)k across…

A: a) find the outward flux of the vector field Fx,y,z=x3i+y3j+z3+xzk across the surface of the region…

Q: The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y" +…

A:

Q: Evaluate the iterated integral. Triple Integral: (Outside to inside) Integral from 1 to 7, Integral…

A:

Q: A watermelon is in the shape of the ellipsoid whose equation is given by 6x2 + 3y2 + 2z2 = 6. If it…

A:

Q: Which of the following functions form a fundamental set of solutions of the differential equation y"…

A:

Q: a. y₁ = x³y + xy³; (x² + y²) dx - xy dy =0 0-X²

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

A: We need to determine and classify the critical points of the function: f(x, y)=4x2y-2x-y2.

Q: Find the Fourier series expansion of the following periodic function: -2<t<0 0<t <2 t, f(t) = {_3

A:

Q: Use the Comparison Test to determine if the following series converges or diverges. 1 Σ n=1 2 2n +…

A:

Q: .[ -x, y) ] Use the method of Lagrange multipliers to find the extreme value(s) of 2² + y² subject…

A:

Q: Verify that the given functions y₁(t) = t and y₂(t) = test satisfy the corresponding homogeneous…

A:

Q: At time 0, Cheryl deposits X into a bank account that credits interest at an annual effective rate…

A: Solution:

Q: From this graph, Find the volume around the X-axis (Use π = 3.14). y = x (0, 0) (1, 1) y=x² R

A: Please find attachment

Q: Which of the following is NOT a subspace of M22? None of them W is the set of matrices of the form W…

A: Definition of subspace : Let V be a vector space over a field F and W a subset of V. Then W is a…

Q: 8. Evaluate the following: (6 marks) (a) log₂32 (b) log12 576-log124

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

Q: For the following Lp values, find k Lp = 8.41 k =  d =  Lp = 2.4 k =  d =  Lp = 3.77 k =  d =

A:

Q: a) Given two matrices A 1 2 3 -2 1 4 and B = 3-1 0 UTM 2) 1 0 1 1 1 2 By using Adjoint method, find…

A:

Q: Define a relation D on the set of real of numbers as follows: Vx, y ER, x Dy ⇒ x-y is rational…

A:

Q: 5. Use the following property of the definite integral to estimate the definite integral: f/ cos x…

A:

Q: 10. A carnival Ferris wheel with a radius of 5m makes one complete revolution every 24 s. The center…

A: 10. Given: Radius of the carnival Ferris wheel is 5m. Time taken to complete one revolution is…

Q: Pure water has a pH value of 7.0. How many times more acidic is milk, with a pH value of 6.4, than…

A: Given that:      pH value of Pure water = 7.0      pH value of Milk            = 6.4

Q: The auxiliary equation for the given differential equation has complex roots. Find a general…

A:

Q: Use the Laplace transform to solve the given differential equation subject to the indicated initial…

A:

Q: Express In (2) in the form a + ib. (Simplify your answer completely.) In(z) = BRITK In( 4√2 ) + 1 (…

A:

Q: ! %A1. The solution of the exact differential equation (2xy² - 3)dx + (2x²y + 4)dy = 0 is: x²y²-3x =…

A:

Q: 1. Solve the following linear differential equations with constant coefficients:

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: The solution to the Initial value problem a" + 2x + 10x = 3 cos(4t), x(0)=0, x'(0) = 0 is the sum of…

A:

Q: In evaluating a double integral over a region D, a sum of iterated integrals was obtained as…

A:

Q: □ Use the definition of integral to prove that for = f'/h 1/x if X FO (x) is NOT if x=0 Riemann…

A: Consider the given function, fx=1x      if x≠00        if x=0 Here we need to prove that f is not…

Q: Show that the vector field 1 F(x, y, z) = (- :)= (-2: 25³ sinh (2y − 1) - x²y is conservative by…

A: If a vector field F→(x, y, z) is conservative then there exists a potential function f(x, y, z) such…

Q: 2, x=0 3. (4 points) Let f: R2 → R be given by f(x, y) = 3, x=2 and R= [0, 2] x [2, 6]. Prove from…

A:

Q: Question 1 a. Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) = x² +…

A:

Q: 3 The following differential equation x³ x ³ (¹) ³ - homogenous D.E. True False -y=0 is a first…

A:

Q: Reduce the ff. matrices to its reduced row echelon form. 3 -2 4 -3 8 2 1 -7 4 1. A = 2 1 1 02 -3 1

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: A snail is at the foot of a flight of ten steps. Everyday it will climb up three steps and climb…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: A baseball team plays in a stadium that holds 60000 spectators. With the ticket price at $9 the…

A: We have to find the maximize revenue.

Q: Which system is represented in the graph?  y x2 – 2x + 4 y ≤ x2 + 4

A:

Q: Given any integers a, b, and c, if a-b is odd and b-c is even, what can you say about the parity of…

A:

Q: Use Stokes's Theorem to evaluate  Integral of the curve from the force vector:  F · dr. or the…

A:

Q: The following differential equation x³ homogenous D.E. True False -y=0 is a first order

A:

Q: Consider the statement: For all integers a, b, and c, if alb and blc then alc. The statement is…

A: We have to find if a divides B and B divides c then a divides c is true or not.

Q: Find a bases for all four the row and column spaces of matrix A sh -21 -2 0 2 -8 4 [1 A = 2 2 Lo 0 3…

A: given matrix A=103-222-2002-84 lets find row echelon form using row operations

Q: Match functions a-f with the appropriate graphs A-F. a. r(t) = (t, -t, t) c. r(t) = (4 cos t, 4…

A: We need to plot the parametric curves for the functions: d. r(t)=2t, sin(t), cos(t) e. r(t)=sin t,…

Q: Find an equation for the graph above.

A: Start with y=sin(x) then change its period increase amplitude then shift towards negative y-axis.