Inverse Functions beduined Let f: R→ R be defined by f(x) = 3x +2. Show that f is bijective and find f-¹.

Q: -> -->> u, v and w are three non-coplanar unit vectors and a, ß and y are the angles between u and…

A:

Q: 64 If y = cos ax, prove that У У1 У г Уз У4 У5 |=0, where y Уб У7 Ув d' dx' у.

A:

Q: Problem I Determine for which values of the real parameter a the following matrix is not invertible.…

A:

Q: Question 32 Solve the problem. Find the general solution of the homogeneous system below. Give your…

A:

Q: 3. Given: region R below bounded by the graphs of y = √, xy = 1, and 3x = 4(y + 1) (1,1) R (4,2) (2,…

A: We know that the area of a region between the curves is computed using the double integral. We have…

Q: From the 7 choices, select all that apply span{ |} + { 1 C -4 } span{ span{ span{ 1 O {0} 1 -1}+{0}…

A: Subspace must contains zero vector with respect to addition. Affine subspace is not consider here.…

Q: press the improper rational transform: 3 X(z) + 1 + z 8 ms of a polynomial and a proper function N

A:

Q: As part of a drug trial, a survey was done to gather information about the participants' experiences…

A: Participants had Nausea denoted by A.  Participants had Dizziness denoted by B.  Participants had…

Q: Question 3 ( Consider the differential equation x²y" - 3xy' + 3y = 2x³ – 3x². x³ are = (a) Verify…

A: x2y''-3xy'+3y=2x3-3x2

Q: Problem II Consider a linear transformation L₁ : Rª → R³ given below and a linear operator L₂: R³ →…

A:

Q: (s+2) s(s-3) b) L{tª(3−2e-³t)²} = a) £¯¹ { L c) L-1 = s+5 (S-1)²+9 ? ||

A: First we will do partial fraction decomposition whenever required then use the formula to find…

Q: Let B be a 2 x 2 matrix such that 7B²-5B+31 = 0. Is B invertible? It so, what are the eigenvalues of…

A:

Q: Question 1 Given the differential equation 2y" - 14y' +24y = 2e-3x a) Classify the given…

A:

Q: Use the Linearization Theorem to classify the equilibrium point y = 0

A: To Linearization  dydt=ycos(4πey) and classify the equilibrium point y = 0.

Q: Consider the following matrices: 0 0 d11 d21 0 0 d12 d22 0 0 0 0 0 с 0 0 --- D 0 €11 €12 €13 0 €21…

A:

Q: Question 15 Find the work done by F over the curve in the direction of increasing t. F = Zi + -j +…

A:

Q: Question 27 Using Green's Theorem, find the outward flux of F across the closed curve C. F = xyi +…

A:

Q: Find the Fourier series on the interval (-, π) of teh function 0, −π < x < 0, 0 < x < π. f(x) = {…

A:

Q: Consider the function f(x) = (x² + x²) + yx₁ X2 subject to 2x₁ + x₂ = 1 Find the range of values of…

A:

Q: -x' + y + z = x-y' + z = x+y-z' = (x(0) = y(0) = z((

A:

Q: 7. What will happen if we add the constraint: (a) x₁ + x₂ + x3 ≤ 9 (b) 2x1 + x3 ≤ 6

A:

Q: (a) How many nonnegative integer solutions are there to the equation ₁ + x₂ + x3 + x₁ = a? (b) How…

A:

Q: please sir solve parts  1 and 2, thanks alot sir

A:

Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

Q: A) Find x{(e-51-7)²} L B)[ Use the definition to evaluate the Laplace Transform of the function 2,…

A: FIRSTLY WE USE AN IDENTITY, a-b2=a2+b2-2ab ⇒e-5t-72=e-5t2+72-14e-5t⇒e-5t-72=e-10t+49-14e-5t AND THE…

Q: 9. For the following data find a right, left, midpoint and trapezoidal Riemann sum with 3 equal sub…

A:

Q: 45 If y=1+ 2 a3x² a ₁ (x-a₁) a₁) (x − a₂) (x −a3) [.. X X a2x (x-a₁) (x − a₂) +... to (n+1) terms, s…

A:

Q: Question 8 Determine whether the matrix is in echelon form, reduced echelon form, or neither. 12 5…

A:

Q: 4. Find q as a function of time if in an LC circuit given by the differential equation La + q = E(1)…

A: Given differential equation is: Ld2qd2t+1Cq=E(t)Putting the given values C=1×10-4F, L=1H,…

Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

A:

Q: 65. (1,0, 1,0), (1,1,1,-1), (1,2,3,0).

A:

Q: To find a particular solution for y" - 6y' + 9y = x² + 10 with the method of variation of…

A: The given differential equation is a second order non-homogeneous differential equation with the…

Q: Let T be the linear transformation that is reflection across the line y = √√8x in R² followed by a…

A: Given, T be the linear transformation that is reflection across the line y=8x in R2 followed by a…

Q: A trough is 5 meters long, 2.5 meters wide, and 2 meters deep. The vertical cross-section of the…

A: Given that the trough is L=5m long, W=2.5 wide, and 2 m deep. The trough is full of water. We need…

Q: 26. Claim: At least one of the last 20 years was not among the top 20 hottest years on record. To…

A: This is a question from the set theory.

Q: If f(x)= (1+x) 1 (1+2x)b (1- (1

A:

Q: f(101) f'(101) 100 49 If f(x)= II (x− n)n(¹101-n), then find n=1

A:

Q: Find the work done by F over the curve in the direction of increasing t. F = ti + = j + k ; C: r(t)…

A:

Q: 1. Determine whether the given set of functions is linearly independent on the interval (-∞0,00).…

A:

Q: 5. A college dean has received the following results from a department chair about MTH 123, which is…

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

Q: Question 12 Compute the product or state that it is undefined. 5-3 || Undefined -3 4 -3 8 2 -4 8 [-2…

A: Remark: Let A and B are matrices of order m*n and n*p. Then multiplication of A and B is possible…

Q: If a₁, 92, a, are in arithmetic progression, where a > 0 for all i, then show that 1 √a₁ + √a₂ 11 +…

A:

Q: Assuming in GF(2) perform the following polynomial division: x² + x6 + x² + x³ + x² + 1 divide by x³…

A:

Q: Question 2 Suppose that a is the area of a disc with radius r which is expanding in time t measured…

A: Given: A disk with radius r which is expanding w.r.t time t  with area a. (a) To Express: dadt in…

Q: PROBLEM #3: t+1' The park is concerned about the number of invasive insects found along their hiking…

A: Given Data: Problem -3 Mt=30tt+1Et=240t+6 Problem -2 Polynomial function : hx=ax4 + 52x3 - 3x2 - 16x…

Q: (a) On what interval(s) is h(x) increasing? O(-3,11) O (-1,5) U (9,11) O (-2,2) U (7,11) O (-3,2) U…

A:

Q: Question 23 Evaluate. The differential is exact. (2,2,2) (1, 1, 1) 0 1 07 O 8 5 2z8 3z8 dx - x3x3…

A:

Q: Find the potential function f for the field F. Here you can assume that the vector field is…

A:

Q: Using Lagrange interpolation, find the value of y at x = 8 Given y(0) = 18, y(1) = 42, y(7) = 57 and…

A:

Q: The Fourier transform of f(t) is F(w): = 6e-6jw wj 7 7+ Using the Convolution Theorem, find f(t) in…

A: As per the question we are given the Fourier transform of the function f(t) as F(ω) And we have to…