1 J = [ exp(-x²)dx Evaluate J by means of Simpson's rule with n = 2m = 10 and h = 0.1 Evaluate J by means of Simpson's rule with n = 2m = 20 and h = 0.05

Q: What is the volume in cubic units of the solid formed when the region (x-1)^2 = 20-4y, y = 1, y = 3,…

A:

Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A:

Q: Assume that is differentiable on a ≤ x ≤ b and that f (b) < f (a). Show that f' is negative at some…

A:

Q: Identify/Find the surfaces of the following equations by converting them into equations in the…

A: The given problem is to convert given cylindrical coordinates equation and spherical coordinates…

Q: 1.6 2.5 0.3261 0.08422 3.5 0.01596

A: Given as,

Q: Find the volume of the solid generated when the region ? bounded by the given curves is revolved…

A: 7 Given that an oil tank in the shape of a sphere has a diameter of 60 ft. We have to find the…

Q: (b) Find Fourier cosine transform of f(x)= 1 0<x< 1/ -1<x<

A:

Q: 9. The inverse of an element a of Z under the operation * defined as a*b = a + b - 1 is A. a - 2 C.…

A: Solution :  Options (B) is correct

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = -197 1 -13 10 5 8-6…

A:

Q: Solve: Revolve about the (a) x-axis and (b) y-axis the area enclosed by y² = x and y = x³

A: The given area is enclosed by                         y2=x  and  y=x3

Q: Find the solutions if k = -1 for 7 N Kx +y+kz=K² ky +z Kx +4 -1 = = = K th + X 2

A: This question is relqted to system of non homogenious equations.

Q: 4. Use the method of undetermined coefficients to find a general solution of the equation y" - 2y" -…

A: Given that,     y''' -2y''-4y'+8y=6xe2x Let y=Aemx(≠0) is a trial solution of the homogeneous part…

Q: (j+ 2)² = j=11 || B 11 first step 2nd step 3rd slep 4th step answer final

A:

Q: 5. The state-space representation for 2x" + 4x + 5x = 10e" is D = +² го 98

A:

Q: 1. The vector v has a magnitude of 5 meters and a direction of 60°. Find the magnitude of its…

A: We have to find the vertical and horizontal component of given vector.

Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2 + 1,…

A: Please find answer below:

Q: 5. Use Cartesian coordinates to evaluate JIJ ² av where D is the tetrahedron in the first octant…

A: As there are multiple questions with subparts, I am doing the first question only as per the…

Q: 5. Use the matrix exponential (as done in class. Do not use generalized eigenvectors) to solve the…

A:

Q: Find the solution of the given initial value problem in explicit form. 75 ㅠ sin (2x) dx + cos(7y) dy…

A:

Q: Prove using direct proof. Include explanation.   If n is an even integer, then 7n + 4 is an even…

A:

Q: Set up the triple integral that will give the following: a) the volume of R using cylindrical…

A: We will use relation between cartesian and cylindrical co ordinate system  x= rcosθ , y = r sinθ and…

Q: √3-i. i. Express w in polar form. ii. Find all the roots of 25 = √√3-i in polar form. Show all the…

A:

Q: What is the y=x^2 4 and O 1/4 01/2 1 3/2 Ο ΝΑ x-coordinate of the centroid of the plane region…

A:

Q: What is the volume in cubic units of the solid formed when the region bounded by y = 2x + 1, x-axis,…

A: This is a problem of the volume of rotation.

Q: Let y = T-97 –3 and i = 5 7 4 -2 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2…

A:

Q: 1. Round 12.083 to the nearest tenth. 2. Round 1.98 to the nearest tenth. 3. Round 0.8693 to the…

A:

Q: Determine the constants a, p, yo and y'o so that 3S +3 Y(s) = (s + 2)² is the Laplace transform of…

A:

Q: -. Prove (A ʼn B) U (Ã – B) = B, using truth table

A:

Q: Let f and g be the following functions. f: N→ P(N) - {0} defined by f(x) = {n: n € N and x ≤ n ≤…

A:

Q: 1: Add the following matrices. -1 2 13 -60 a) + b) 0 1 -2] 12 3 + 000 0 0

A:

Q: Evaluate J by means of trapezoidal rule using n = 10 and n =20: 1 = [*exp(-x²) dx Evaluate J by…

A: We need to find the value of J=∫01exp(-x2) dx using the trapezoidal rule with n=20 and n=10

Q: What is the y=x^2 - 4 and O 1/4 1/2 01 3/2 Ο ΝΑ x-coordinate of the centroid of the plane region…

A:

Q: What is the x-coordinate of the centroid of the plane region bounded by y = 2x + 1, x + y = 7, and x…

A: We have to find the x-coordinate of the centroid.

Q: Use Simpson's rule to approximate the integral f5 +7dx O 0.51879836 O 0.81879835 O 0.61879835

A: The given integral ∫01x5+73dx , n=4 The Simpsons rule formula is given by…

Q: 0.The inverse of the elements of A = {0,1,2} under a*b = (a+b) modulo 3 are A. 0' = 0, 1' = 1, 2' =…

A: The given set A under * is the set ℤ3A=0,1,2a*b=a+b modulo 3Consider the table, Eg:…

Q: 3 3 -3 5) Based on the Wave diagram, Find a0. 6) Based on the wave diagram in no. 5, Find bn when…

A:

Q: earned $6,500 this summer and plans to invest her money for 10 years, and she has two options to…

A:

Q: 1.1 Expand √1-² to three terms using the binomial theorem. Simplify the terms. 1.2 The relationship…

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

Q: y-coordinate of the centroid of the plane region bounded by 22 What is the y = 2x + 1, x + y = 7,…

A:

Q: 4. Use the method of undetermined coefficients to find a general solution of the equation y" - 2y" -…

A:

Q: 10 Σ 15m³ n=m first step 2nd step final answer

A: The given series is                          ∑n=m1015m3 To find this sum we shall use the formula of…

Q: 1. Find the general solution of dy dx + y = x

A:

Q: 3. Find the surface area of the parallelepiped with adjacent edges u = (4, 7, -8), v = (-2, 5, 11),…

A: Solution :18

Q: Consider the function f(x)=2 sin(π 2 (x−3)) +6  State the amplitude A, period P, and midline. State…

A:

Q: f(t) = (C + 1)te Bt sin At

A:

Q: Question Eight y s 7 6 5 m X The diagram shows the shaded region bounded by the curves y = x² + 2, y…

A: Solution :

Q: 2n+2 Σ (3k + 2n) = = k=0 = || ⠀ first step 2nd step 3rd step final answer

A: We know that 1+2+3+4+......+n is equal to n(n+1)/2

Q: 1. Use the power series 1 Σ(-1)n-1-1, x + 1 n=1 to find a power series, centered at 0, of the…

A: It is known that 1x+1=∑n=1∞-1n-1xn-1or1x+1=1-x+x2-x3+x4-⋯        ....1

Q: What is the center of gravity of the solid formed when the plane region bounded by y^2 = 4x in the…

A:

Q: contrapositive proof. Include explanation.

A: Given that if n is an even, then 7n + 4 is an even integer.