In x x→ x-1 25. Find lim " ln x In x given that log₂ (x+1) ≤· -≤1-— as x⇒1¯¯. x-1 X

Q: [39] (a) u(t-3)(t-8) +2u(t-7) cos(xt) (b) (i-8 t-8+2 cos(xt) t<3, 3<t<7, 127.

A:

Q: Numerical analysis Find an interval [a,b] that contains the root of the function f(x)=x^3-4x-9?

A:

Q: Let f: C be defined by f(z) M that 2²/2, if Z+0; if z=0 0. } Show the real and the Cauchy - Riemann…

A:

Q: can both parts be written on paper please, if you can only do one then let it be part

A:

Q: Let A, B and C be nonempty sets and let f : A → B, g: BC and h: B → C be functions. For each of the…

A:

Q: Find the Taylor polynomial of degree 3, centered at a = 2 for the function f(x) = √x + 6.

A:

Q: 9. 10. Identify the vertical and horizontal asymptotes f (x) = 1 a) VA: x = 4, HA: y = - 2 1 c) VA:…

A:

Q: Problem: G Let's verify that gravity is conservative (F is just a force field) and then find the…

A:

Q: First, compute the gradient of the function p(x,y)=√√9-x² - y². Then evaluate it at the point…

A: ; We have to find .

Q: the Euler-Lagrange equation for the fur y² + 1 -dx. y/2

A:

Q: Find the eigenvalues and eigenfunctions for the following boundary value problem (with À > 0). y" +…

A:

Q: How many functions are there from the set {1, 2, 3} to the set {7,8}. Enter your answer =

A: and We have to find how many functions are there from the set  to the set .

Q: 2. Solve the simultaneous congruences x = 4 (mod 5) and 2x = 3 (mod 7)

A:

Q: We are interested in the first few Taylor Polynomials for the function f(x) = 4e + 9e¯ centered at a…

A: Given: The function . To find the Taylor polyomials of degree one and degree two for the given…

Q: 5 d²q dt² + 10 dq + 1 q = 25 sint dt 0.1

A:

Q: = e. Convert from multiplicative to additive notation: (1) a²b³; (2) a=²(b=¹c)² =

A: Here we have to convert the multiplicative notation to additive notation of1) a2 (2) a-2(b-1c)2…

Q: Apply the method of undetermined coefficients to find a particular solution to the following system.…

A: (.) Given system is,         let (.)  Let  is a particular solution then it satisfies the given…

Q: A2. Use Bordered Hessians to determine the sign properties (definiteness) of the following con-…

A: To determine the definiteness of the quadratic forms subject to the given constraints, we can use…

Q: For matrix (0 -1 0, 1 0 0, 0 0 1), show that [adj(A)}^-1 = (1 / det(A))*A = adj (A^-1)

A: The objective of the question is to prove the identity adj(A)^-1 = (1 / det(A))*A = adj (A^-1) for…

Q: Several oil companies are jointly planning to build an oil pipeline to connect several southwestern,…

A: Given information:Given a network of 10 cities in the southwestern, southeastern, and midwestern…

Q: Consider the following initial-value problem. (y² cos(x) - 3x²y - 6x) dx + (2y sin(x) − x³ + In(y))…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: A healthy child's systolic blood pressure p (in millimeters of mercury) and weight w (in pounds) are…

A: Given the table,wln⁡(w)p473.8589634.1496784.361021014.621101264.84117We need to find the…

Q: Apply the method of undetermined coefficients to find a particular solution to the following system.…

A:

Q: 2. i) State the equations of the horizontal asymptotes of the functions below. ii) Verify the end…

A:

Q: A piece of wire 16 ft long is cut into two pieces. One piece is made into a circle and the other…

A: A piece of wire  long.One piece is cut into square and other piece is made into a circle.We have to…

Q: 5. For the system of differential equation ¹ = A x, with coefficient matrix given by, (i) A = =…

A: Note: As multiple questions have been asked, so only first question i.e., (i) has been solved…

Q: Suppose a subspace is spanned by the set S of vectors shown below. s={[G]-[-2.]} S Find a subset of…

A:

Q: Let f(x) = 3 + cos (5 a) where 0 < x < 2π. Next we do a Fourier series expansion of f(x). The…

A:

Q: 2. a) Differentiate the function Q(p) = -2₁√/p³ (²-√). b) Hence or otherwise, determine Q'(1).

A: Derivative using product rules

Q: 5) Given T:RR defined by T(x)=x+1 Determine if it is a linear transformation.

A: For given transformation, T(x) = x+1 We have to find whether it is linear transformation or not.

Q: Solve. Identity and reject any extraneous roots. log(m+2) - 1 = -log(m-1)

A:

Q: In a field plane PG(2, F), a line ax+by+cz = 0, not through the vertices of the triangle of…

A: To show that , , and are concurrent, we can use Ceva's theorem. Ceva's theorem states that in a…

Q: 2. Let V₁ a. 14 -2' b. V₂ = " 16 10 spanned by B. Note that B is an orthogonal set. -49- 35 7 -28_…

A:

Q: Suppose a subspace is spanned by the set of vectors shown. ((-24].[23]) Find a basis for the…

A:

Q: Determine the potential function for the region inside. a rectangular trough of in finite length…

A: The potential function V(x,y) satisfies the Laplace equation,Vxx+Vyy=0,      0≤x≤b , 0≤y≤aFrom the…

Q: For n, ke Z, k0, we denote by A(n, k) the set of integers that are congruent to n modulo k: -2k+n,…

A:

Q: 8. A vector field F is given in cylindrical polar coordinates by F(p₁6, 2) == cos(7²)₂ Find the…

A:

Q: ///₂² 2² + y² +2²dV, where E is the ball: z2 + y² + 2² ≤ 16. +³+2²dV Use spherical coordinates to…

A: We have to evaluate the triple integral  by using spherical coordinates, where  is the ball: .…

Q: Problem 3. Let u be a smooth solution of Lu aªÏ µij V = |Vu|²+ Au². Show that Lv ≥ 0 in № if λ is…

A: To show that in for sufficiently large let's compute :Now, since is a smooth solution of , the…

Q: n the Konigsberg bridge problem, the islands are joined to the mainland by several bridges. Are…

A: No, these bridges are not really "bridges" in the graph theory sense. Bridges are edges that, when…

Q: Consider two groups, G 1 ​ and  G 2 ​ . Group G 1 ​ is defined as {1,a,a^2 ,a^3 } with operation ⋅ ⋅…

A: this basically states the following that any 2 cyclic groups of the same order are isomorphic.

Q: 4. Consider the binomial (a + b)^n and calculate what is asked below. a) Use De Moivre's theorem to…

A:

Q: The Temporary Help Company must provide secretaries to its clients over the next year on the…

A: Given information:Quarterly Schedule:Spring:  secretary-daysSummer:  secretary-daysFall:…

Q: 4. (i) Show that 2 is a primitive root mod 112 = 121. Hint: Use the criterion given by Lemma 6.4 and…

A:

Q: Consider a differential equation of the type dy dt f(t,y), (1) where ƒ is a function that may depend…

A: Note- In this question part (a) and part (c) alredy solve by experts and good explain each part we…

Q: 1) Suppose T is a linear transformation of TH=2-3x + x² and T[3] =1-x² T[2¹] and T Determine. R² to…

A:

Q: -2 8 6

A: The graph has no branch for negative value of x.So, Given function is not defined on therefore, we…

Q: For the following graph, explain, giving reason for your answer, why an Euler circuit exists.…

A: Given graph

Q: dx So 1+x²n 0 = π/2n sin () 2n

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Sketch the graph of the function below and determine its Laplace transform. u(t-6) -u(t-8) Click…

A: