Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and (x²+1)g'(x)+ 3xg(x) = e2+ x, on R If f is known, what is g in terms of f?

Q: 1- Solve the problem P.D.E. u, = uxx + sin(nx) + sin(2nx) fu(0, t) = 0 lu(1,t) = 0 u(x, 0) = 0 0 <x…

A: Solution

Q: 2.66 Let fn(x) = z for all r E R. a) Find the pointwise limit of fn. b) Does f converge uniformly on…

A: Convergence and uniform convergence of the sequence

Q: Let P denote the set of all functions f on [0, 1] such that there exists at least one point x E [0,…

A:

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: given curves y=225-x2  , y=9 find the volume of the solid that results when the region enclosed by…

Q: . You are designing a spherical tank to hold water for a small village.The volume of liquid it can…

A:

Q: er the ideals I = (x, y²) and J = (x- 2y) in Qlr, y)- %3D %3D

A:

Q: The rate of increase of the temperature of water being heated in a kettle at any timet is modelled…

A:

Q: 5. Find the canonical prime factorization and solve for No. of positive divisor and sum of positive…

A:

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: The volume of a solid rotated around the y-axis can be calculated using the "Disk Method" The disk…

Q: Let fn(x) = sin" x and let 8 > 0. a) Prove: fn converges uniformly on [0, 5 – 8], but not uniformly…

A: The given function is fnx=sinnx. To find: (a) fnx=sinnx uniformly or not on given domains.…

Q: Recall that the differential equation for the instantaneous charge g(t) on the capacitor in an…

A:

Q: choose the appropriate answer

A:

Q: Let R be the region bounded by the functions f(x) = –2x² and g(x) = -8 as shown in the diagram…

A: Given curve f(x)=-2x2  and g(x) = -8For intersection point    f(x) = g(x)so     -2x2 =-8        x2=4…

Q: Convert the Partial Diff equation to canonical form and find the general solution a²u + cos?x- ду?…

A: Sol

Q: se Indirect Proof to prove that if a and b are both positive, and a2 < bi

A:

Q: 2. Exprear the vector W ==28 ay + 28 az, in spherical Coordinates at Q(r= 14, O. e = 38° $ = 128°)…

A: Given,Vector,w=-28 ay+28 azr=14,θ=38°,ϕ=128°We need to express the given vector in a spherical…

Q: Example 2: A food product is made from soybean meal (50% protein, 10% moisture) and corn flour (10%…

A:

Q: By using shell method, find the following volume a. y = (x-3)2 and line y = -2x + 6 about x axis

A: Sol

Q: у- 4y/ + 4y — е?" (12л? — 6х); у(0) — 1, у/ (0) — 0 %3D

A:

Q: jlog(4- ji') (541.5) In log(4ejn) j log(-7)

A:

Q: Determine the 1st and 2nd degree Taylor polynomials L(x, y) and Q(x, y) for f(x, y) = e-a²-y°…

A: Given function is fx,y=e−x2−y2cosxy. We have to find the first and second degree Taylor polynomial…

Q: When recording live performances, sound engineers often use a microphone with a cardioid pickup…

A: The given equation is r=16+16sinθ. The microphone is at 8 m from the front. Quadratic equation is…

Q: 17. zdy + (x sec² () - y) da = 0

A:

Q: Use the future value formula to find the indicated value. FV = $4512; n= 15; i = 0.08; PMT = ? PMT =…

A:

Q: sider the system i1 = xỉ – 2x1x2 and i2 = -x2 + xỉ Find the first few terms in the power series…

A:

Q: In the puzzles below each letter represents distinct digit in a decimal scale. Identify the digits.…

A:

Q: 2.57 † Let S = functions on [a,b]. Show that if n e N and if ao, a1,..., an are not all 0, then it…

A:

Q: The rate of increase of the temperature of water being heated in a kettle at any time t is mod the…

A: We will solve the differential equation by using variable separable method and then use initial…

Q: | (ах с) (2а+b—4c)| (αx b) . c If a = 2i + 3j – 5k,b = 3i + 7j - k and c = 5j – k. Calculate %D

A: Solution

Q: The following information is provided for a one compartment drug X following first-order elimination…

A: Sol

Q: Show tht if x is an integer, then gcd(x+1, x2-x+1) divides 3.

A: Sol

Q: 2a] aS a product Of irreducible polynomials.

A:

Q: 3. Use Mathematical Induction to prove that 4 + 10 + 18 + ... + n (n + 3) = [n .. (n + 1) (n +5)] /3…

A: The solution is given as

Q: Find the greatest common divisor g of the numbers 1819 and3587 and then find integers x and y to…

A:

Q: The orbit of a satellite revolving around a planet is an ellipse with the center of the planet as…

A: The standard equation of ellipse is x2a2+y2b2=1. In the above equation, a is the half-length of…

Q: Consider the series n+5 Determine whether the series converges, and if it converges, determine its…

A:

Q: The displacement s of a body in a damped mechanical system, with no external forces, satisfies the…

A:

Q: cosh In(-3+2j)] a. -1.6154 + 0.9231j b. 1.9396 + 0.0741j c. 18.3972 + 0.8193 d-15.3227 10.1998j

A: option a is the correct answer

Q: 4. Let A = |2 5 2 2 (a) Find the projection matrix P for R(A). (b) Let b = |9. Find the least…

A:

Q: what is the spanning fuzzy subgraph ? And give examples

A: Given : Spanning of fuzzy graph is mentioned in given example. We need to tell that what if fuzzy…

Q: (i) ( Let y: [a, b) → C be a curve. Explain what it means for y to be: (a) piecewise smooth; (b)…

A: Sol

Q: Real Analysis Prove the theorem: Let {fn} be an equicontinuous, uniformly bounded sequence of…

A:

Q: 2. Which of the following statements is always true about a real m-by-n linear system, where m <n.…

A: We have to find the true option .

Q: 2. Write the Kolmogorov backward equations for a birth-and-death process with birth rates d; = 3(i +…

A:

Q: You are considering two job offers: Job 1 is a full-time position that pays $58,000 annually and Job…

A: Concept: Gross income = net income - deductions.

Q: ) Let F(x, y) = (3x² + y²)i + 2xyj. (a) Test if F is a conservative vector field. (b) If F is…

A:

Q: С. Show that f (x) = x³ + 4x2 - 10 = 0 has a root in [1, 2] and use the Bisection method to…

A:

Q: 2. Sole Laplace's equation for a rectangular region (0<x<1, and 0<y<1) subject to the given boundary…

A: Solution

Q: 6. Which of the following is the graph of r =' 2 - sin 0

A: We have to find the graph of r= 6/(2-sinθ)

Q: A quadrivector AH has components (1, 1, 1, 0, 1)' in the system S. Calculate the T components of AH…

A: