Q2: If f(x) is Riemann-Stieltjes integrable function with respect to g(x) on [a,b] and if f(x)dg(x)=0 for every function f(x) which is monotonic on [a,b] . Prove that g(x) must be constant on [a,b].

Q: Using the formula f(x+th)-f(x) t f'(x)= lim: h→0 and admitting the existence of the derivatives of…

A: a) f:R3→R2 defined by fx,y,z=x2+y , x+y+z2 also given z=1,1,2 , h1,1,2 using the formula…

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Q: Find the volume of the solid generated by revolving the region bo x-axis. 16) y = √ , y=0, x= 1, x =…

A: Introduction: To determine the volume of specific solids, one can utilize the disc method, an…

Q: U U a. For any p= [1,00), any A,BER and XERd, we have ||(A+B)x||ps||A||pl|x||p+||B||pl|x||p. dxd b.…

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Q: Problem 3. Let T: R2 R2 be a linear transformation that reflects points through the line 2 = -1 and…

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Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives fr and fy at the…

A: Given: fx,y=x-1·y13 We have to determine whether fx,y is differentiable at the point x,y=1,0

Q: (b) (c) Explain the differentiability of f on R by using definition. 1 Let f' be the first…

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Q: Define S to be the following relation on R[x]: S = {(f, g) = R [x]²: (x + 1) divides (g - f) in R[x]…

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Q: Find the following expression, if not defined, give the reason why. a.) 14B – 3B

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Q: Question 5. Apply Laplace Transform to solve the following Differential Equation when x(0) = x'(0) =…

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Q: I. Use the Divergence Theorem: (² F. ds = Ifv. Fav SSS E = to calculate the flux of the field F…

A: Divergence theorem uses  Double integration converts into triple integration.

Q: Example (2.3): solve the initial system ordinary differential equations by Runge- Kutta method f₁=y'…

A: Given that y'=1-x+3z ,y0=1, x∈0,1z'=x-siny ,z0=2 , h=0.2 at x=0.6

Q: 3. This question concerns the L metric d and the L¹ metric e on a) Calculate d(f.g) and e(f.g),…

A: Consider L∞ metric d and L1metric e on C[0,1]. (i) To Find: d(f,g) , e(f,g) for  f(x)=1+x , g(x)=x2.…

Q: A graphing calculator is required for the following problem. Gasoline is pumped into a cylindrical…

A: As per company guidelines we are allowed to solve maximum three sub-parts at a time so i am solving…

Q: L[sin at] (e) Laplace Transform: F(s) fe-st f(t) dt. (f) Convolution: (f* g)(t) = f f(0)g(t – 0)do.…

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Q: Write an equation for the hyperbola shown in the graph The equation for the hyperbola above is = 1.…

A: The equation of hyperbola with vertical traverse axis is y2a2-x2b2=1 From the given graph, we have :…

Q: Players A, B, C, and D are dividing an estate using the Method of Sealed Bids. There are three…

A: A sort of auction in which bids are not seen until the auction day is a sealed-bid auction. The bids…

Q: Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives fr and fy at the…

A: Given  f(x,y)=x-1.y1/3 As per your request I go with part b The linearization of f(x y) is…

Q: Consider the following. x=t², y = In(t) (a) Eliminate the parameter to find a Cartesian equation of…

A: Introduction: Parametric form is another representation of curve in Euclidean geometry. Here, the…

Q: Find the critical point set for the given system. dx dt dy dt = x-y = 6x² + y² - 1 ... Find the…

A: Given system is dxdt=x−y dydt=6x2+y2−1. For critical point equate dxdt=0 and dydt=0.…

Q: +6 12+ +10+ 1- 1. 4- 3- X0X 1-

A: We have a 5×5 kenken puzzle. We will put values from 1 to 5 in the cells satisfying the given…

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A: Integral = (lnx)^7/7+c

Q: Solve the IVP. (35 53 X' = X with X(0) = - (4).

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Q: The following graph is not planar. a b d e

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Q: Write an equation for the ellipse Type the left side of the equation in the box below. G

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Q: Let f(x, y) = y²exy. (a) Find the normal vector to the graph of f(x, y) at (0,1,1). (b) Find the…

A: Given That : function f(x,y)=y2exy To find : Normal vector to the graph of f(x,y) at (0,1,1)

Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

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Q: Show that the following series is not absolutely convergent 1+k² (-1)*. 2-k km3

A: As per our company guideline we are supposed to answer only first  qs, kindly post remaining qs in…

Q: 1. Linear independence and rank Consider 4 column vectors: 0·60-0- and 2 with x, y, z ER. i.…

A: The answer for the second part as asked is as follows,

Q: Calculate the area between 0 and 7 /2 of the r = 10 + (1 + cos²0) curve, the x and y ordinates of…

A: Given that r=10+1+12cos2θ To find the area between the interval 0,π2 using Simpson's rule where…

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Q: Let N₁ (h) be the approximation of f'(xo) with some numerical differentiation scheme depending on h.…

A: Given that N10.1=0.4974N10.05=0.5190

Q: • Let: X₁ (jw) = 2nd(w) + nd(w − 4ñ) + ñ8(w + 4π) • Use the inverse Fourier Transform to find x₁(t)…

A: Introduction: Like other integral transformation, Fourier transformation has also its inverse. In…

Q: Compute the line integral [(yze²v² + y² + 2 − 2x) dx + (xze²v² + 2xy) dy + (xye²³² +x+32²) dz, where…

A: We have to compute the line integral ∫Cyzexyz+y2+z−2xdx+xzexyz+2xydy+xyexyz+x+3z2dz, where C is the…

Q: Let (z-a)" dz where a € C and the parameterization of the curve is a = {|z| = r}. Apply the…

A: Hint: The statement of fundamental theorem  of complex analysis is: If a continuous function f has…

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A: Given f(2) = 1  we are using tangent line approximation for finding f(1.7), f(2.02)

Q: please explain to me why the first line gives (1+ k + 1)

A: We have to take (k+1)! common from the terms (k+1)! and (k+1)(k+1)! to get the required form.

Q: For each nN, consider x,, H (a) (b) 71 X with x E R. Define the sequence {gn} by 8n(x) = f(x) = 1…

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Q: 7. Consider the Helix: r(t) = (R cost, R sint, Rt), 0 ≤ t ≤ 2π for R a constant. A. Calculate the…

A: This is the question from Vector Calculus.

Q: Select every element X of Z₁2 that is a solution to the equation X² + [1]12 X= [0] 12. [0]12 [1]12…

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Q: Problem 15. Let A = 2 1 0 0 1 (a) Find all eigenvalues of A. (b) Diagonalize the matrix A (i.e. find…

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Q: For the following exercises, consider the construction of a pen to enclose an area. 7 You have 800…

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Q: -f(x) = x cos x, -π < x < π Find the Fourier series for the following functions:

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Q: 2. Use f(x) = 2x + 5 and g(x) = x^2 + x - 6 for following combinations. A. (f+g)(x) = B. (g-f)(x) =…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Use the trapezoid rule to approximate the following integrals: (using n = 4 subintervals) a.…

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Q: Question 3 For each nEN, consider xn (a) (b) n == X with x ER+. Define the sequence {gn} by 8n(x) =…

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Q: Ex3 i) ii) Let T: C ([0,1]) → R f → f(0) If C ([0,1]) is equipped with the sup-norm, show that T is…

A: As per the policy, we are solving first question. Please repost it and specify which question is to…

Q: b) A field mouse population satisfies the Initial Value Problem: 0.5p-400, p(0) = 600. (a) Find the…

A: a) Hint: The given initial value problem is, dpdt=0.5p-400, p(0)=600