We can compute an improper integral as a limit over regions of a different shape: SS S₁₂e-²-³ dady = lim 11.² e a-00 Sa -2²-y² dxdy where Sa is the square [-a, a] x [-a, a]. Use this definition to conclude that: (1 e ² dz) (edy) = ₁ -2-² dx T

Q: given function then derivative Now dz dr dz d४ sing rcass-38³ He Have to find it's dz dr = dz 5 = 5…

A: We have to transcribe the given text in the digital form.

Q: Which of the following transformations are linear? Select all of the linear transformations. There…

A:

Q: Solve the following initial value problem. 2 -2 -2 1 0 1 2 -2 -2 x = X, x(0) : 0 2

A:

Q: Find the mass and the center of mass of the following solid: The tetrahedron bounded by the planes…

A: The given problem is to find mass and center of mass of the given solid tetrahedron bounded by given…

Q: Let A and B be independent events with P(A) = P(An B) = P(AUB) = 1 ·|6 1 and P(B) = Find P(An B) and…

A:

Q: Suppose that iz2 7 - / 512² +2¹ dz. where is the rectangle with vertices at 5 +8 i and 2 + 8 i and 2…

A: Curve C is a rectangle with vertices  5+8i, 2+8i, 2-8i, and 5-8i. (a) We have to draw this contour…

Q: J\~). Question 2: Given the function f(x, y) = sin(x + y), at the point P(π/3, π/4) • What unit…

A: Given a function  fx ,y=sinx+y at a point Pπ/3 , π/4. To Find : a) Unit vector which leads to the…

Q: Let B = {b₁,b2, b3} be a basis of R³ where Find the vector V. b₁ Enter the vector V in the form [C1,…

A: The given basis is, b1=-153,b2= 225, b3=44-1. coordinates of vector v relative to basis β is,…

Q: 3. Let V be a finite dimensional vector space and let (.,.,) be an inner product on V. Suppose that…

A:

Q: 500 4 2-4 -204 001 2 1 1 0 0 4 -2 40 0 -2 0-1 0 20 0 1 2 00 5 100

A:

Q: Find the Moments (Mx) for the lamina that occupies the region D and has the given "Density" function…

A:

Q: Your client has been given a trust fund valued at $1.64 million. She cannot access the money until…

A: The trust fund valued $1.64 million. The money will be available from 65 years old after 15 years.…

Q: Bob makes his first $1,700 deposit into an IRA earning 7.4% compounded annually on his 24th birthday…

A: Given: Regular payment PMT=1700 The annual rate of interest i=7.4% =0.074 Time periods n=18

Q: SOLVE STEP BY STEP THE FOLLOWING ODE IN DIGITAL FORMAT y' = 3(y - 10)

A: We have to solve the ODE  y'=3(y-10)

Q: 7. Which chart represents exponential decay? a) c) x y x y 0 480 1 2 4 240 120 30 0 1 2 4 480 380…

A:

Q: Use "Polar" coordinates to find the "Volume" of the given solid. a) What is the maximum bound of the…

A: a) Consider the given equations of the paraboloids, z=5-2x2-2y2 and z=4x2+4y2 The graph is shown…

Q: Find the intervals on which​ f(x) is​ increasing, the intervals on which​ f(x) is​ decreasing, and…

A:

Q: uppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given…

A:

Q: Use the comparison theorem to determine whether = is convergent or divergent. Hint: Compare it with…

A:

Q: "S[. 10. 10 2x-1 16 S[cate 7XH - 21 7² dx = 5 In (2x-1) - 3 -зе + 7x+1 15 Cos (2x+3) B (2x+1)+ - 8…

A:

Q: Fran's collection of seven albums includes one country album. Fran will choose four of her albums to…

A:

Q: Using the Laplace transform pairs and the Laplace transform theorems, derive the Laplace transforms…

A: If F(s) is the Laplace transform of f(t), then it can be written that: Lf(t)=F(s). Using the table…

Q: Let U = { 10, 11, 12, 13, 14, 15, 16}, A = { 10, 11, 13, 14). Use the roster method to write the set…

A: U={10,11,12,13,14,15, 16}  A={10,11 ,13, 14} Here A' = set of those elements which belongs to U but…

Q: 2. Examine the tables below and answer the questions that follow. . Table A Year 0 1 2 3 4 5 6…

A:

Q: Let f: R² → R be defined by f((x, y)) = 6x- -9y - 9. Is f a linear transformation? a. f((x1, y₁) +…

A:

Q: Define T: R2 R² by T(x1, x2) = (x2 +3, x₁ + 4) (a) Find u € R² and L = O(R²) such that T = T₂ o L.…

A: Given: T:ℝ2→ℝ2 by  Tx1,x2=-x2+3,x1+4  , x1,x2∈ℝ2 To find:  (a) u∈ℝ2 and  L∈Oℝ2 such that T=Tu∘L.…

Q: (b) (bn), where bn := n (1 +212) " for all n € N. Hint: Consider bn.

A:

Q: Identify the type of reasoning employed in the following arguments as INDUCTIVE or DEDUCTIVE. 1.…

A: Inductive reasoning means to arrive at a general statement from specific observations. Deductive…

Q: Write each statement in symbols. Let p=" Depression is public health issue. and let q= "Not enough…

A: Given that, p=Depression is public health issue. q=Not enough people seek treatment. To write given…

Q: Consider the following system of three linear equations in three unknowns: x₁ + x₂ + ax₂ = 1 = x₂ +…

A:

Q: I Let f: RR be the function defined by f(x) || if x = 0, and f(0) = a. Is there a choice of a so…

A:

Q: Find the generating function of the sequence {ak }ko defined by a= 2 if k is an integer such that 0…

A: Generating Function: The formula to find the generating function for the sequence…

Q: Translate

A: In given statement, Unless is used in middle of the statment and hence it is strong sense. Hence…

Q: Obtain the differential equation of the family of plane curve described and sketch at least 5…

A:

Q: Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special…

A:

Q: Niagara falls has a flow rate of 2400 cubic metres per second. How many Olympic-sized swimming pools…

A: The  time taken by a flow flowing at a particular flow rate to fill a volume can be determine by…

Q: 1. Evaluate the following integrals: C. dx √√(4x²+4x-3)*

A:

Q: Assume that an is a Cauchy sequence. Prove that the sequences 3an and a² are Cauchy sequences as…

A: Given: (an) is a Cauchy Sequence. To Prove: 3an and an2 are also Cauchy sequences.

Q: e resolve this!

A:

Q: 8. A manufacturer can sell a certain health supplement for Php1,100 per unit. Its total cost…

A:

Q: 3. Consider the set X = {a,b,c} and the function f: X→ X defined by the rules f(a) = b. f (b) = a…

A: The set X=a, b, c and the function f:X→X defined by the rules fa=b, fb=a, fc=b. We have to find the…

Q: MPZ 18. Jane claims that she can help show that 6n + 3n9n is true by first choosing one positive…

A:

Q: If f(x) is given by f(x) = sinh √2x2, compute for the errors for each approximation for each…

A: The given function fx=sinh2x2. The approximations, x 1 2 3 4 5 f(x) 1.3911 2.9034 5.8982…

Q: An experiment is conducted for which the sample space is S = {S₁,S2,S3,S4,S5}. Is the following…

A:

Q: 2. Obtain the differential equation of the family of plane curve described and sketch at least 5…

A: Given : y-a2=4cx To sketch a family of curves.

Q: 2u" (t) 10u' (t) + 12u(t) = 4t -

A:

Q: (c) Find the value of √a²-x² Sa giving your answer in terms of a. 1+ 2(x + y) x² + y² dx dy,

A:

Q: From the sample space S = {1, 2, 3, 4,..., 15} a single number is to be selected at random. Given…

A:

Q: Prove that if lim f(x) is of the form X-C g(x) 0 Write a 8-& proof. then lim ƒ (x) g(x) X-C =18.

A:

Q: Let B be an m x n matrix and let AB be a k x n matrix. If rank B = rank (AB), show that null (A) ~…

A: