et flk) = - ** = **(- at k+1 dt k+1 1 Let f(k) %3D 1 Prove that f(k) satisfies 0

Q: What does Cauchy's EU Theorem 6.2 guarantee for the IVP dy/dt = -(y^2)/2t , IC: (t_o,0) a solution…

A: The given equation is  dydt=-y22t I.C. =t0,0

Q: Example: Examine the convergence of COs x dx (ii) / x'e*² dx

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Q: Suppose that for each i such that 1 <i<N one has / f(1)dt = i Ji-1 What is / f(t)dt if N = 87?

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Q: Calculate the maximum long-term harvest for a population satisfying the DTDS rNt Nt+1 - hNț. 1+ kN{…

A: Given Nt+1=rNt1+kNt-hNt              (1) Given r=1.5 and k=1

Q: tinuous at t= 0, it is continuous at every other point. 3 If the autocorrelation function R(t) of a…

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Q: Solve the DEQ given the initial condition (-2,5). Graph it on the slope field. 1 + Let g(x.y)=dy/dx…

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Q: 30. Find the continuous function f(t) satisfying csin z for all r. 2+ f(t)dt = sin2015 /3

A: According to Leibnitz rule:

Q: Find the radius of convergence for: (- 1)"x" Vn + 7 TL=1

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Q: Find the lower bound for the radius of convergence for (x2 + 6x+ 10)y′′+ (x2 −4)y′+ x2y= 0 about x0…

A: Since given point x0 is an ordinary point of the given equation obtain the singular points and thr…

Q: (a) Suppose that f is differentiable, positive and decreasing on (a, b] and has no critical points.…

A: Given problem:-

Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: 1 1 Σ = 0. Vn - 1+ yn converges because lim Vn – 1+ yn 2=1 True False

A: We have to check

Q: By using the substitution t² determine the convergence of = S ∞ dx (x+1)√√x*

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Q: Show that f„(x) = x" (1– x") converges pointwise V x € (-1,1]. Is f„(x) converges uniformly?

A: When a sequence includes a variable, it becomes a sequence of function. A sequence of function can…

Q: Since f(x, y) = 1 + y² and ðf/ðy = 2y are continuous everywhere, the region R in Theorem 1.2.1 can…

A: Given data: We are given that y=tan(x+c) is the family of the solution using initial value y(0)=0

Q: f fn → ƒ uniformly and the functions fn have only jump discon- sinuities, prove that f has only jump…

A: Here we use epsilon delta proof

Q: Calculate the formal asymptotic expansion of the initial value problem x' = -ɛx +1, x(0) = 0. up to…

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Q: How to prove that the function h(y)= sum_{m+1} ^infinity (m+y)/(m^2+y^2) converges to a continuous…

A: We are given a series given as, hy=∑m+1αm+ym2+y2 We need to show that the above series is…

Q: Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1,…

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Q: Use the Limit Comparison Test to determin 8" + 1 n = 1 9n + 1 g"+1 lim =L> 0 n-- O converges

A: Given series is ∑n=1∞ 8n+19n+1 find whether the series is convergent or divergent

Q: If the function f is continuous on [0,00) and | f(x)dx is convergent, then there is a possibility…

A: If the function fIs continuous on [0, ∞) and ∫1∞f(x)dx is covergent, then there  is a possiblility…

Q: The approximation of the root x' of the function f(x) = 2x² + 5 - e* in the interval [3,4]accurate…

A: Consider the given information.

Q: sin(²) En=1 is 18 √n a. 1 b. 12/12 c. Converge d. Diverge d O C O a O b O

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Q: Show that the following method is convergent, and determine it's global order of accuracy. 1 At Yn+1…

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Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

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Q: 2 Q/if the function fc)=ĕ is not Continuous at T where =TIL x<T foint the fourier Scries of fcxeě is…

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Q: 1. For r < 1, define fn(x) = ²x. (a) Prove that for x < 1, k=1 ƒ(x) = lim_ƒn(x) = 84x x(1+x) (1-x)³…

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Q: Let fn(x) x + n a. Show that fn(x) converges pointwise [0, 0). on

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Q: 2.1 Show that a sequence of Riemann-Integrable functions fn(r) converges uniformly to a…

A: As per our company guidelines, we are supposed to answer only 1st question at a time. Kindly repost…

Q: Suppose f(x) > 0 and g(x) > 0 and that | f(x)dx diverges. If f(x) > g(x), what can we conclude about…

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Q: (x) = x and f2 (x) = sin (x) sin Wron

A: f 1 (x) = x and f2 (x) = sin (x) sin Wronskian functions that are linearly independent show using.

Q: What is the radius of convergence from > Vn (x – 1)" n=0

A: Given power series is ∑n=0∞nx-1n The given power series converges if…

Q: -5 1 10) Determine whether the improper integral diverges or converges: ī dx Vx-1

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Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: 1 Given f : [2, 0) → R, Prove that fn(x) = converges uniformly to f(x) = 0. 1+ x"

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Q: Find the interval of convergence ofS f(x) dx where f (x) = (-1)+(x-6)" %3D E

A: Given problem is :

Q: What does Cauchys EU theorem guarantee for The IVP:  dy/dt = -(y)^2/2t,  IC: (to,0)

A: Ft,y=-y22tDomain:{t,y∈R2:t≠0}∂F∂y=-ytDomain:{t,y∈R2:t≠0}∴function Ft,y is continous.So there exists…

Q: The Fixed Point Iteration method always converges when f(x)-D0 is transformed to x=F(x). True O…

A: The fixed point iteration theorem is very significant in solving an equation numerically. Here, we…

Q: Let F : R → R be given by F(x) = (x – c)*, where x € R is a constant. Suppose that we apply Newton's…

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Q: If fn : R → [0, 0) is a sequence of integrable functions, fn + f a.e. as n → 0, and S fn + 0. Prove…

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Q: (z - 1)dt + (1 – t)dz %3D

A: (4) Given differential equation is z−1dt+1−tdz=0......1. We have to determine the whether the…

Q: 3. Find upper bound for error of linearization of the following function at given point Po(1,2), 4.…

A: We can solve this by using partial derivative formula

Q: Assume x and y are functions of t. Evaluate dy / dt for 4xey = 8 - ln 64 + 6ln x, with the…

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Q: -if f₁ (t) properties of Fourier transfor eat alt) JF.T = $ fit) ējut dt = - feat. ejust dt е ماز-…

A: Topic:- calculus

Q: If g is a differentiable function and g(0)=0 and g'(0) > 0. a) Prove that f(x) = 1/2 (integral from…

A: We will use the basic knowledge of differential and integral calculus to answer both the parts of…

Q: Let f : [0, 1] → R be a continuous function. Show that the sequence of functions 1 fn (x) = ,x +1 +…

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Q: Sought: An approximate solution of the equation 2x – tan(x) = 0 in the interval (1,1.5]. Let 4(x) =…

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Q: Consider a zero mean stationary Gaussian process X(t) with autocorrelation function Rx (t). Find the…

A: Introduction - Autocorrelation - It is a mathematical representation of the degree of similarity…