25. Let f: R→ R and let f(x) > 0 for all x € R. Show that f(x) is strictly decreasing if and only if the function g(x) = 1/f(x) is strictly increasing.

Q: (c) xy' + 4y = 3x², y(2) = 4

A:

Q: 13.3. Let y be the curve given by z(t)=t+it², 0≤ t ≤ 2. Evaluate £121²dz.

A: Here given that z(t) = t + it2, then dz = dt + 2itdt

Q: Let V = span{v1 = (1, 1, 2), v2 = (0, 1, 1), v3 = (-1, 0, -1)} be the subspace of R^3 endowed with…

A:

Q: A nuclear cooling tower • The tower is 320 feet high The base measures 268 feet across The top…

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

Q: Examine the following graph of a function modeling damped harmonic motion. Find the equation for the…

A: The graph shows a damped harmonic motion. Here, the following features are prominently displayed:…

Q: Find a piecewise smooth parametrization of the path C (the edges of the triangle in space with…

A: we will use line integral for function F along the curve r(t)  ∫CF.dr = ∫ab F(r(t)) r'(t) dr

Q: d) f(x) = (x²+1)/(x²+2)

A:

Q: Find the values of x, where the following power series, Σn=1n²+1' is absolutely convergent,…

A:

Q: Assume a particle moves along the top branch of the parabola y2 = 3x from left to right going at a…

A:

Q: If AT y = b has a solution and Ax = 0, is (x¹ b = 0) or (x y = 0)? Justify your answer…

A: Given ATy=0 has a solution and Ax=0. We need to determine whether xTb=0 or xTy=0 is true.

Q: 4. An interpolating polynomial of degree 20 is to be used to approximate e-² on the interval [0,2].…

A:

Q: Let TV → V be an operator with V a f.d.i.p.s. Show that A is an eigenvalue of T if and only if X is…

A: Given that T:V-->V is an operator with V is a finite dimension inner product space.  As V is…

Q: ΤΟ 1 10 1 1 1 1 0

A: We find the characteristic equation, the eigenvalues, and bases the eigenspaces of the Matrix as…

Q: If f is the Fourier series of g(x)= √3, [16-², -4 < x < 0 then 0≤ < 4 f(2)=¯ + 2 [(0) cos (1 x) + (…

A: Given:  gx=3,   -4&lt;x&lt;016-x2,   0≤x&lt;4To do:  Find Fourier series of g(x) and call it f(x).…

Q: Prove that these are convergent but not absolutely convergent using calculus but with proof…

A: Given series a∑n=2∞-1n+1nlnnb∑n=1∞-1n+1n13lnn2

Q: The ellipsoid and sphere 2x2 +52 +22-22808/441 2² + y² + 2² +32+2y-5z+2798/441 = 0 are tangent to…

A:

Q: Problem #4: Problem #4: SS F Use the divergence theorem to find the outward flux of the vector field…

A: The given problem is to find the flux of the given vector over the given surface bounded by given…

Q: 70. Displacement from a velocity graph Consider the velocity function for an object moving along a…

A:

Q: 3. A cosine function has a maximum value of 1 and a minimum value of - 5, and a phase shift of 2,…

A:

Q: 11) Test the series for con convergence E (-1)^ sin² (3n) n n=1 = Compute the derivative d br an…

A:

Q: solve the initial value problem   xy' + 4y = 3x^2, y(2) = 4

A:

Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: We find required equation of tangent line to the given curve.

Q: = Given that the matrix A has eigenvalues X₁ = 1 with corresponding eigenvector ₁ = = and X₂ = -4…

A: We use definition of eigenvalue and corresponding eigenvector of matrix A.

Q: 3x + 1 Prove: lim 2−0r+1 = 1.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: dy dx = 9x + 2y 9x + 2y + 2 y(-1) = -1

A:

Q: Use the table to determine if the pattern of change is linear or exponential. If the change is…

A:

Q: Select the partial differential equation that can be used to model this scenario. J²u Ju A.k- dz² B.…

A: A String of length L is secured at both ends. The string is released from rest with initial…

Q: Determine the intervals on which the given function is concave up or down and find the points of…

A:

Q: Write the following equations in first-order form so that they could be simulated with ode45. a) mx…

A: Note: The important thing to remember is that ode45 can only solve a first order ODE. Therefore to…

Q: dy Solve the given initial-value problem. The DE is of the form = f(Ax+By+ C). dx dy dx 9x + 2y 9x +…

A: Given differential equation is of the form dy/dx = f(Ax+By+C)

Q: Let C(n) be the constant term in the expansion of (x + 7)". Prove by induction that C(n) = 7" for…

A:

Q: a. C. 2 1²2 [132] 0 b. 2 d. -2-1

A:

Q: The linear tranformation L defined by maps P4 into P3. (a) Find the matrix representation of I with…

A: The given linear transformation, L:P4→P3 is defined by Lpx=15p'-13p''. a) We have to find the matrix…

Q: 2. a. Use a computer algebra system to evaluate the following integrals. fsi i. sin x cos 2x dx ii.…

A: Given :  a Following integrals : i ∫sinx cos2x dxii ∫sin3x cos7x dxiii ∫sin8x cos3x dx b∫sinax cosbx…

Q: 9. Let F be the function such that F (n) is the sum of the first n positive integers. Give a…

A:

Q: ind the eigenvalues of A, given that A= nd its eigenvectors are he eigenvalues are 7 -4 8 -1 8-58 -1…

A: We use definition of eigenvalue and eigenvector of a matrix to find required eigenvalues.

Q: Solve the given initial-value problem. d²x dt² x(t) = + 9x = 8 sin(3t), x(0) = 3, x'(0) = 0

A:

Q: Show every step of the problem. That is the only way I will know how you solved the problem.…

A:

Q: Q1D. Consider the following graph: a C f d e How many vertices are there in the graph? How many…

A:

Q: Use linear differential equation method

A:

Q: h (x) = 2x² − 8x +9 - Show your work for each question to receive credit. 1. Does the parabola open…

A:

Q: Tell whether or not you can (a Hernating series test) Enter D if the series diverges by this test…

A:

Q: An interior decorater wants to mount a picture that is 5 inches by 7 inches unto a wall. A picture…

A: Let, the uniform width of the picture is m inch.  Then, dimensions of the picture with the frame is…

Q: Find the area of the region bounded by the astroid x = 16 cos ³t, y = 16 sin ³t, for 0≤t≤ 2.

A:

Q: Q2A. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f} E = {{a, b},…

A:

Q: A = 060 4 1 2 20 04

A:

Q: Problem #1: Problem #1: Use Stokes' Theorem to evaluate F F dr where F = (x + 7z)i + (3x+y)j +…

A:

Q: Use Theorem 7.4.2 to evaluate the given Laplace transform. Do not evaluate the convolution integral…

A:

Q: Stokes' theorem to write a line integral that is equal to the surface integral curl F. dS, whe

A: