a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

Q: 3. A 2 cm long metal wire with thermal diffusivity ² = 4cm² s¹ is used to conduct heat in a machine…

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Q: f(x) = sin (2x)| -T≤x≤0 0<x<*

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Q: b) A drawer contains 14 white and 14 black socks, all unmatched. Ali is in a rush to school and has…

A: The pigeonhole principle is the base of counting along with the fundamental theorem of counting.…

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Let S be the quadric with equation    4x2 - (y-3)2 + 4z2 = 4 ⇒x2 - (y-3)2/4 + z2 =1

Q: Let V be n-dimensional vector space over c en for any n scalars ₁, ... , E F there-

A:

Q: EXERCISE 7.5 A. Write the converse, inverse and contrapositive of the following statements. 1. If I…

A: We need to convert the given statements into it's converse , contrapositive and inverse. We know…

Q: het Ley) = y(4) + y (3) _ 7 y (2) _y (¹) al solve: Lys = 36t-24et > b) solve: hy)= 36t-24et 2.2t c)…

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Q: V be a finite dimensional vector spac field F, then there is a natural isom "onto V**. V**. |

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Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

A: Given ,  Parabola be  x2 = 2py and 4py-p2-x2=0 4py-p2-x2=0x2 = 4py-p2x2 = 4py-p4 At intersectionx2…

Q: Allow A be the point with Cartesian coordinates (6, 9), and D be the plane curve with parametric…

A: The slope of the tangent to the curve: y=fx at x=a is f'a. The point-slope form of a line that…

Q: Find the volume of the solid generated by the region bounded by x² + y = 6, y = x, y = -2 and x = -2…

A: Here we see for a small depth then extend it to all the region.

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral…

A: Let  I= ∫π4π2ln(tanx)dx Here, a=π4 , b=π2 , f(x) =ln(tanx) Step size h=b-1n=π2-π410=π410=π40 Then…

Q: d) y'= 4y-3x 2x-y

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Q: B = 0 -2 12 4 −1 -1 3 4

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Q: Find the area bounded by the curves y - x² = -3,x+y = 3 and y = 0.5x.

A:

Q: 4. 2x₁ + X₂ X3 3x₂ + x3 -2x3 2x₁ + x₂ + x3 L = Answer X₁ X4 = 7 x4 = -3 = 2 2x4 = 8 x₂ = M U = x3 =…

A: Given,                  2x1 +x2 - x3 - x4 = 73x2 + x3 - x4 = -3         -2x2  = 22x1 + x2 + x3 -2x4…

Q: Consider the surface S given by 22² +2y² = a + 1 = 0. (a) Find the equations of the traces of S on…

A: A quadric surface is a graph of the function of two variables x and y in the three dimensional space…

Q: Given any two Euclidean spaces E and F, w ension m, for any linear map ƒ: E→F, we have Ker f = Ker…

A:

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: Solution

Q: 7). Construct a formal proof of validity of the argument. a). p^q P→ ~(q^r) s➜r i. S

A: We prove the given argument by using rules of inference.

Q: Given f(x) = -x³-7x² - 8x + 16 = (x+4) (4-3x-x2²). Find the (a) intervals on which f is decreasing…

A: Follow the steps.

Q: 2. Find the Fourier series of the given function f(x), which is assumed to have the period 2L. f(x)…

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Q: Which hyperbolic functions are increasing on their domains? A. tanh x and cosh x are increasing on…

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Q: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7 -3 4 0 -71 A-2 1-1 4 6 010-3 -5 3. SOLVE THE SYSTEM…

A: A=7-340-721-146010-3-5 WE HAVE TO FIND LU FACTORIZATION.

Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

A: graph of the area bounded by curves x2+4x+4y+8=0⇒y=-1-(x+2)24 and y=-2 is   Volume of the solid…

Q: Show that the three functions: f₁(x) = ex-8f2(x)= ex, f(x) = 4(2x-2) are linearly dependent.

A:

Q: If the graph is Hamiltonian, find a Hamilton cycle; if the graph is Eulerian, find an Euler tour.

A: deg(d)+deg(h) = 4+4 =8 where d and h are not adjacent. Since deg(d)+deg(h) is not greater than the…

Q: Advanced Math b) The curve y= y = x³ + px² - 12x has a stationary point when X=-4 5 i) Show the…

A: Follow the steps.

Q: Finding the Determinants using Elementary Row Operations E = 2 1 3 1 10 11 0210 0 1 23 1 1 -2 -7 0 1…

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Q: a) 2 B3] b) 001 010 101

A:

Q: Given: quadric surface S with equation (y - 3)² 1 (a) Determine and identify the traces of S on each…

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Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

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Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: We can solve this using given information

Q: 3. Let A and B be sets in the universe U.Prove the following statements: (a) A = A. (b) AB if and…

A: Solution :-

Q: 4. Which of the following is a Legendre's equation? a. (1-x²)y" - 2xy' + 3y = 0 b. (1-x²)y" + 2xy' -…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use secant method to find the root of x^3 –x^2 – 3x – 3 with two initial points xa=3 and xb=2 and ∈=…

A: We have f(x)=x3-x2-3x-3 iteration formula for secant method is: xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn)…

Q: Q5: Consider the following subsets of real plane R²¹ Determine with graph: 1-Arewise connected A=…

A: Here we have a common point in both of the sets. Also thos two sets are individually connected.

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

A: First graph the region.

Q: Village C (he is at Village A): A → Bk → C for k Marvin is deciding a path from three (3) routes to…

A: Solution : Conditional probability: probability of A given that B already happened. P(AB)=P(A∩B)P(B)…

Q: Determine the solution to the given ODE: = (1 + 2z) √ over the interval from x-0 to 1 using a step…

A:

Q: Consider the vec Ř(e) {{cos (1²₂), c² - 2². ²+/-) t# -1 <-1,4,-27, t = 11. (1.) show that I is…

A:

Q: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7 -3 4 0 -7] A = 2 1 -1 4 6 010-3 -3 -5 1.3 USE…

A: To get row echelon form aply the operations only rows and such that the resultant matrix is upper…

Q: (f. g)'(2) =

A: Real valued function: A function whose domain and codomain are subsets of the set of real numbers ℝ…

Q: Solve the linear system using both gauss-jacobi and gauss-seidel 3x + y = 1 2x + 5y = 6 a. using…

A:

Q: 5. The von Bertalanffy equation is defined by the ODE W'(t) = aw (t)* -BW (t) where is a constant…

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Q: 5. Consider the vector-valued function R(t) = (t³ — t, 2t², 2 — 2t²) a. Find ||R'(t)|| (Simplify…

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Q: 4. Evaluate ryz dV, S is the solid in the first octant S bounded by the cylinders x² + y² = 4 and x²…

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Q: List the elements of each set where N= {1,2,3…} a.) A = {x∈ N | 3 < x < 9} b.) B = { x∈ N | x is…

A: Set-builder form The set contains the element that has single property in all Roaster form The set…

Q: 14. Write the given system of differential equation as a matrix equation X' = AX. dx = 2x + 3y, dt…

A: System of differential equations: A finite set of differential equations with one independent…

Q: 2. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Y = {y|y= 2x, x € Z} Enumerate: a.) X - Z b.) Xu (YNZ) X…

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