Example 11.10. Solve the boundary value problem u, u under the conditions u(0, t) = u(1, t) = 0 and u(x, 0) = sin nx, 0≤x≤1 using Schmidt method (Take h = 0.2 and a = 1/2).

Q: A space vehicle flies into a gravitational force field F(x, y, z)=-y(b²2² + a²y²)i + (b²r² + a²y)j…

A: The work done by a force field is equal to the dot product of the force field and the displacement…

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: We have to Find the hydrostatic force on one end of the trough.

Q: x1/2 dx and using the substitution = x 1/2, the resulting integral takes the form: u= 4u -du 4-4² S-…

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Q: Example 10.28. Solve the differential equations dy dz = 1 + xz, = -xy for x = 0.3, dx dx using…

A: Here we need to use runge kutta method. please find solution below:

Q: Given the formula, S n =a 1-r^ n 1-r what is the sum of the first nine terms of the geometric series…

A: Note: The geometric series has to be 324, -108, 36, -12,....., Otherwise there will be no common…

Q: Find the area bounded by the curve y=x3. -x2+3x and the line y=x. 16 4

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Q: Consider the equation d - 2y = 0, y(0) = a. Let I = (-1, 1). Which statement below is NOT true? -…

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Q: Let T: X→→→→→ Y be a linear operator and dim X = dim Y=n<∞. Show that R(T) = Y if and only if T¹…

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Q: Define R as the region bounded by the graphs of the function f(x) = x3 , the x-axis, x = 0, and x =…

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Q: Please show full solution for thumbs up!

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Q: A={1, x, x²} and A'= *-·A·D· Let Z: P₂ → R³ be the linear transformation given: a + 2b + c…

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Q: (b) Let B = {₁,...,n} be a basis for an inner product space V with inner product (,). We can nxn…

A: It is given that B=b1, b2, ⋯, bn is a basis for the inner product space V with inner product .. The…

Q: A van costs $25,000 and has an expected life of 6 years, with a salvage value (Residual Value) of…

A: Given that: Actual cost of the van = $25,000 Expected life = 6 years Salvage value = $1,500 To…

Q: cos² (x) + cos² (2) cos³ (x) S .dx

A: As per the question we are given an indefinite integral which we have to solve.

Q: y dy Find using the substitution +5= √√y+2. √x+2 A²/(√y+2-5)(-5√/y+2+y+21) +C 3 ® ²/(√y+2-5)…

A: ∫ydyy+2 Substitute, u+5=y+2 Then , du=12y+2dy ⇒2y+2 du =dy ⇒2u+5 du =dy and y=u+52-2=u2+10u+23

Q: In Exercises 23-26, use the shell method to find the volumes of the solids generated by revolving…

A: Note. 1: Since you have asked multiple questions, we will solve the first question for you. If you…

Q: The sum of a positive factor of pq is p+q+pq-1 None of them p+q+pq p+q+1

A: The factors of pq are 1, p, q, pq. So, the sum of the factors is 1+p+q+pq i.e. p+q+pq+1 Therefore…

Q: 2. y" - y = x, y(0) = 1, y'(0) = −2, h = 0.1 from x = 0 to 1.

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Q: A value= B value= Horizontal shift:

A: Given,          f(x)=-4cos(x)+2

Q: acid, HO₂C H, the first ionizatio Ka₂=4.2. Why is the second carboxyl g

A: Acids will sour substances with the pH values less than 7. Acids can donate their protons. There are…

Q: using the following: Line 1: x = 2 + t, y = 1 + t, z = 4 + 7t                                 Line…

A: Given of lines are: Line 1: x=2+t, y=1+t, z=4+7tLine 2: x=−4+5s,  y=2−2s, z=1−4s

Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

A: Solution

Q: Л Define R as the region that is bounded by the graph of the function f(x) = -3√3 sin (x), the…

A: To find the volume of the solid that is obtained by revolving the region bounded by below curves…

Q: Consider the following IVP: y'= 1+4. 1st ≤2, y(1)=2. The actual solution of this IVP is y(t) = t…

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Q: 5. Solve the DE dy d²y xdx² dx - 4x = 0, 1<x<2 with y(1) = y(2) = 0. a) Using weak form and Galerkin…

A: Let us start solving the problem step by step    For the given DE we will start solving by the…

Q: Use a software program or a graphing utility with matrix capabilities to find the transition matrix…

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Q: The graphing calculator window shows the graph of a function f(x) and its derivative function f'(x).…

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Q: Question 12 Calculate the area of the smaller region (to the left of the parabola) bounded by…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y the…

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Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

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Q: 5 Lim 9-5 -4 dx 2 -x²-8x-15

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Q: Using the three-point midpoint formula, find the approximate value of the fist derivative of f(x)=…

A: Given  f(x) = xex The three- point midpoint formula with error f'(x0)=12hfx0+h-fx0-h-h26f3ξ1

Q: xy(1 + xy²) dx = 1 Ans: + y² -2=2

A: Given ode is ,                                                                   xy(1+xy)dydx = 1…

Q: In how many ways can 6 girls and 3 boys sit on a row of 9 chairs in such a way that no two boys sit…

A: we have to solve given problems:

Q: a. Which of the following surface graphs represents f(x,y) = y²? OA.

A: Given, the surface                           z=f(x, y)=y2

Q: Naomi buys a 2 bottle of concentrated juice. She adds water to make 14 t of diluted juice at a total…

A: Given: The total cost of 14 l of diluted juice is R 14.95 and each glass will contain 0.175 l of…

Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

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Q: 7 8

A: Solution

Q: There are three numbers in geometric progression whose sum is 26. If the first is increased by 2,…

A: The arithmetic and geometric progressions are two important rule that terms of a sequence follow to…

Q: a) s> a O a b O C с O d b) s <a c) s = a = { Leat موجود أذا كان d) sza

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

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Q: 2. Construct the interpolating polynomial of degree 4 using divided difference for the data given…

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Q: Answer Questions 8 & 10 please and thank you

A: Note: We are entitled to solve only one question at a time. So we are doing Question 8 only. Please…

Q: Example 35. Using th d²y satisfying the differential equation v(1) = 2. + y = x, subject to the…

A: Here we need to use finite difference mthod.

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y = 4 is…

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Q: Exercises To Solve [No.5] Lim 5 9-5 dx -x²8x-15 D "Cosx dx Sin x+25inx+5 b

A: 5)  Let , I = lima→5 ∫a-4 dx-x2 - 8x - 15 Let , us simplify denominator first ,  -x2 - 8x - 15 = -x2…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y, the…

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Q: ?

A: 1. The measure of arc is twice the angle formed at the circumference, therefore RS⏜=250° Therefore…

Q: find the distance from A(4, 6, -3) to the line x = 3t + 1, y = -t + 3, z = 6t

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Q: 3 3 2 Find the area bounded by the curve y=x²-x² + 3x and the line y=x. 16 4 10 square units 8…

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