2. Give an example of a regulated function f on [0, 1] such that f(x) > 0 for all æ e (0, 1), So f(x)dx = 0, and such that f (xo) > 0 for at least one ro E [0, 1). Is there an example which is not a step function?

Q: 3. Find the maximum and minimum values of a 1 āz - on |z| ≤ 1 (where a with la| < 1 is fixed)

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Q: ´28 – e14z x 0 Determine whether the function f(x) = 14x – 1

A: Solution: Consider the given function is  f(x) = x8-e14x    x&lt;014x-1       x≥0 To check whether…

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A: Given query is to find the derivative of the expression.

Q: Let g(t) be piecewise continuous on [0, ∞) and of exponential order, use the convolution theorem to…

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Q: Is there a sequence of continuously differentiable functions: fn : R –→ R such that fn → x and f. →0…

A: Yes, the sequence is given in step 2.

Q: if f(x) is a continuous function at x = -6 * = 0, then a 1- cos4x x2 If f(x)= { a x = 0 r>0 16+Vx-4

A: a= 8.   See the attachment for the complete solution.

Q: 3 Given the function: f(x) = (1+ x)³/2 . x - 1 Prove that it is increasing on (0, +00) analytically,…

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Q: Let fn E D[0, 1]. Suppose that fh g on [0, 1], and lim fn(1/2) exists. For each x E [0, 1], show…

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Q: Find the absolute maximum and absolute minimumvalues of  f on the given interval.

A: Given equation is Differentiating both sides, we get Now, we will wind critical points of f(t) in…

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A: According to the given information, consider the given function z.

Q: 1. Given that x +1 2x2-1 g(x) Show that the g(x) function is continuous at a = 4.

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Q: (a) Find if y = y (ln r). (b) The function f(z) (In r) is an invertible function (you do not need to…

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Q: of of and Find for the following function. f(x.y) = e xy In (2y) of dy

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Q: If f (x) is an invertible, differentiable function with tangent line y = 4 x + 7 at the point (0, 7)…

A: we have to swap variable for finding the inverse function

Q: Find the Wronskian for the set of functions.{e3x, sin 2x}

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Q: 1. Show (in terms of e – 6) that a function f : [2, 7] → R be defined by f(x) = Vx² + 1 is uniformly…

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Q: Let f(x) = e x if −π < x 6 π. And extend f to a 2π periodic function on R. Determine the…

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Q: 1) Consider the function f(x) = In(x + 5) + x + 5 Verify that the function F(x) = x In(x + 5) is an…

A: Explanation of the answer is as follows

Q: We have found the following Wronskians. W = -e-³x; W₁ =-e-2x(4+ex)-¹; W₂ = e¯x(4+ e*)-¹ We want to…

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Q: Find the Wronskian for the set of functions {e¬*, xe¯×, (x + 1)e-*}.

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Q: 2. If f is a continuous function such that S(t)dt = cos(2x)e* - [e s(t)dt for all x, find an…

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Q: 3. Consider the following formula f (x) = lim n-0 gn +1 Let D = {x € R: f(x) E R}. Calculate f(x)…

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Q: If 0 < f(x) < g(x) for all x and I f(x)dx diverges, then | g(x)dx diverges. 13 Select one: True…

A: Given the statement

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A: The Initial value problem is given as, f'x=-1x+1fx, for  -13≤x≤12                         (1) with…

Q: e +1 Differentiate the function f(x)= In 5x +1 Se+1 3ex+1 Sesz e3x +1 ,5x +1 e 3e3z Sesz e3x +1 5x…

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Q: Show (in terms of e - 6) that a function f : [2,7] R be defined by f(z) = V² +1 is uniformly…

A: In this question, we need to show the given function f(x) is uniformly continuous.…

Q: 8. Given for C[0,1] the inner-product function (f,g)=[f(x)g(x)dx , find ||f|| if f(x) = x+1.

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Q: - if f(x) is a continuous function at x O, then a = 1-cos4x よく0 x? { a If f(x) = r= 0 r>0 V16+ VF -

A: Then to find the value of a if f(x) is continuous at x=0   Since for any continuous function at…

Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: 1. Show (in terms of e – 8) that a function f : R³ → R defined by f (x, y, z) = (2x + 3y + 4z) is…

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Q: a. The function f: RR given by f(x)=x² is twice continuously differentiable in R", and its Hessian…

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: Find the dérivative of the function: f(x)=In(e^x-13x)

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Q: Given that for each a E (0, 1) lim t "(1 – t)"dt exists. Let, this limit be g(a). In addition, it is…

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Q: Consider the following first-order ODE: d = (1+2x) √9, x = [0, 1], y (x = 0) = 1 Using step size of…

A: consider the following first order ODE dydx=1+2xy with x=0,1 and yx=0=1 claim- use step size h=0.05…

Q: 9) The Wronskian of the functions f(x) = -5, g(æ) = 7x² y h(x) = e3 is given by a) W(f(x), g(x),…

A: The details calculation is given below

Q: Please see picture

A: Introduction:Here, MX (t) denotes the moment generating function (mgf) of the random variable X;…

Q: Let f(x) = e* if -n <x< T. And extend f to a 27t periodic function on R. Determine the coefficients…

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Q: Using the generating function, prove the following relation Ph+1(x) + Ph-1(x) = 2xP(x) + P (x) %3D

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Q: Find the global minimum of the function f (x) 1 + x² on the interval (0, co0)

A: Given that f(x)= 1+x2.  And we find global minima on the interval (0, infinity).     Here i attached…

Q: (b) A function f AR is continuous at a point c E A if for any e > 0, unere exists A one 8 >0 but de…

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Q: 4. If R(T) is the autocorrelation function of a stationary process {X(t)} with no periodic…

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Q: a) Evaluate in terms of Gamma function ∫e^(−y^2) y^13 dy   limit 0 to ∞ b) Find ∫f(x) dx limit: 1…

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Q: 1. Consider the function z = f(x, y). If fa(a, b) and fy(a, b) both exist, and they are equal, then…

A: 1. Given: z=fx,y and suppose that fxa,b and fya,b both exists and they are equal and it is…

Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

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Q: 1. (a) Find when t = 0, if e“ cos t = (x + 1)t + 1. dt2 (Ъ) Suppose f is a differentiable function…

A: We hav to find the following conditions and we have to show the given condition

Q: The Gamma Function is defined by [(x) = fx-¹e-tdt, positive integer then prove that for na T(n) = (n…

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