4) Let the composition of two functions f(x) = sin(x) - 2x² + 1 and g(x) = eº be h = fog. At a point x = h(x) is a convex function. h(x) is a concave function. h(x) is a non-decreasing function. h(x) is a decreasing function. 5, Select the true statement(s).

Q: Show that I+J is an ideal of L where I+J ={x+y:x∈I, y∈J}.

A: Given that and  are two ideals of a ring Ideal Test:A nonempty subset A of a ring is an ideal of…

Q: Diagonalize matrix A, i.e. find a diagonal matrix A and nonsingular matrix V such that A = VAV-¹. A…

A:

Q: The matrix 8 4 -4 0 -4 -4 0 has two real eigenvalues, one of multiplicity 1 and one of multiplicity…

A:

Q: 11) a) Approximate (2x² − x −1) dx using midpoint Riemann sum with 8 equal subintervals. 0 b)…

A:

Q: Find the Taylor polynomial T3 for the function f(x) = ln(x) at the number a = 1 OA. (x-1)+(x - 1)² +…

A:

Q: Let S be a linear transformation from R³ to R² with associated matrix 2 - [2²2 2 -3 3 0 3] Let T be…

A:

Q: Let A = A basis for the image of A is 9 -6 6 9 Find a basis for the image of A (or, equivalently,…

A:

Q: bales of hay

A: The cattle at the Clay Farm are fed 4 bales of hay each day.It mentions that the horses are fed 2…

Q: Let [f] = Let f: R2 R² be the linear transformation defined by →>> = 30 B = {(1, 1), (-1,0)}, {(1,…

A:

Q: Find the matrix A of the linear transformation T(ƒ(t)) = 2ƒ' (t) +9f(t) from P₂ to P₂ with respect…

A:

Q: f(x) = 1 on [1,00)

A: Let I be an interval and a function  is said the be uniformly continuous on I if corresponding to…

Q: Prove that the function ƒ : R – {5} —> R - {3} defined by f(x) = 3x +1 x-5 is a bijection.

A: Consider the function  defined by .To prove that f is a bijection, we have to prove that f is both…

Q: find the limits in terms of dz Dr dTheta and explain how you got each likit

A: We have to construct triple integral to find out volume of region bounded by the cooordinate planes…

Q: Show that [1 1 0 0 1 1 0 0 001 1 det ⠀⠀⠀N : ⠀⠀⠀⠀ : 000 0 100 0 ⠀⠀⠀ ... 0 0 00 00 ⠀ ⠀ = 1+ (−1)n+1. :…

A:

Q: Let f: IR →IR be the 2π-periodic function defined by f(x) = (x-π)², x ∈ [0,2π[. 1. Calculate the…

A: The given function  be the periodic function defined by  if .We know that the Fourier series of a…

Q: SOLVE STEP BY STEP DON'T USE CHATGPT 3. Calculate the volume inside the cylinder x^2 + y^2 =4 that…

A:

Q: Prorate the following expenses and find the corresponding monthly expense. Lan pays a semiannual…

A:

Q: The number of arbitrary constants in the general solution of the differential equation: D³( 2D5+ D¹…

A:

Q: Find Z 2 order Sinz + 324 of the order of the zero at 2=0 pode of and 1-cosz 24 ot 2=0

A:

Q: 3. Determine whether the following sets are open, closed, both, or neither. (a) (2,3) U{4} (b) [2,3]…

A: (a) (b)

Q: 4. (i) Show that |(0, 1)| = |R|, where (0, 1) = {x € R: 0 0}. You don't need to prove that the…

A:

Q: (a) f(x₁, x₂) = x₁x² subject to 2x₁ + 3x₂ = 4,

A: For this problem we first write the lagrangian function of the function of the variable and the…

Q: 1. Consider a rectangular tank that is standing on its square base of length 4 meters and a height…

A:

Q: The temperature when the column of mercury is -4 inches long The length of the column of mercury…

A: Let f(x) be the temperature (°C) when the column of mercury in a particular thermometer is x inches…

Q: 5. Let f(x)=√x² if x is rational Zo if x is irrational AR a.) Is f continous at o? bj Is f continous…

A: The given function is .(a)Check either the function is continous at  or not.The function will be…

Q: M = Find the matrix M of the linear transformation T: R³ →>> X1 X2 X3 = R² given by [90]. -6x1 - x2…

A:

Q: Find the area between the two curves: y² = x, x² - 2x + 3y = 2

A:

Q: Find T(x) for the given function at the number a. P(x) = ³x a=0 n=3 0≤x≤ 0.2 T3(x) = 1 + 4x + 8x² +…

A:

Q: Consider a linear transformation T from R³ to R² for which Find the matrix A of T. -[ A = 31 ¹(E) -…

A:

Q: E. For each of the following series, determine whether the series converges or diverges. For those…

A: E (i). Given series ∑n=1∞3n+5n7nA geometric series a+ar+ar2+⋯ converges when |r|<1 and diverges…

Q: Compute w using w= 7 - 3 ||w|| = (Type an exact answer, using radicals a

A: We have to find .

Q: Determine an affine transformation T that maps the large figure to the similar (smaller) figure.

A: To find the affine function we find the point and the transform point From the figure we see that…

Q: Find the maximum value of the function z = 3x + 5y subject to the following constraints. x≥3 y≥2…

A: Given ,Function z = 3x + 5y

Q: Find all least-square solutions to Ar = b where 1 0 110 110 101 101 1 0 1 A = 7 b= = 2 3 6 5 4

A:

Q: The income distribution for a certain country is represented by the Lorenz curve with the equation…

A: It is given that the income distribution for a certain country is represented by the Lorenzcurve…

Q: Let V = R²x2 be the vector space of 2 x 2 matrices and let L: V → V be defined by L(X) = 15 - || =…

A:

Q: The accompanying table shows time-to-speed data for a particular car accelerating from rest to 130…

A: The traveling distance from 0 to 40.1 sec is S=∫040.1v(t)dtWhere v(t) is the speed at the time…

Q: Find the matrix M of the linear transformation T: R³. →>>> R² given by X1 (J- = -3x1 - x2 + 9x3 2x1…

A:

Q: Let F = (yey, xey) and let C be given by: x = sin(t), y = et-¹(1 – cos(πt)), 0≤t≤ 1. Show that is…

A:

Q: If you let R=Z[x] and I = (x^2 -2) be the principal ideal generated by f(x) = (x^2 -2). If r=(2x +…

A:

Q: 2. Prove that the union of two disjoint sets, where one is countably infinite and the other is…

A:

Q: Students at certain university have to pass of one these three courses (MAT102, STA105, and PHY110).…

A:

Q: If 3 does not divide n then 3|2n² +1. If x is a positive prime integer, then x+7 is a composite…

A: We have to prove or disprove the following statements:(a) If 3 does not divide n then 3 | 2n2+1.(b)…

Q: 2. Let a 0 be such that a+h≤b. Prove that there is € (0, 1) such that: f(x+h)-f(x) h Hint: x, h are…

A:

Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save…

A:

Q: If y = (x + 1)(2x - √x), then y' will be 1 A. (x + 1) (2 − √x) + (2x − ——) 2√x B. (x+1) + (2x- √x)…

A:

Q: Question S ze" 121=1 dz use Taylor E ez é½₂ zeź (1 8 n=o Find essential singularites series. ents So…

A:

Q: Let G be a digraph with n ≥ 2 vertices. The graph is strongly connected, and every node has indegree…

A:

Q: Is the value x = -12 the last value of the function's domain is 6 ≤ x ≤ 12 Is the function…

A: In given figure of graph of function,[-6,12) is domain of function. x=12 is not included in the…

Q: The matrices -69-63 A₂ = A₁ = 0 A3 = 0 0 -694-61 , = form a basis for the linear space V = R²X2.…

A: