(x +2 if x 2 1 f(x) =2x - 1 if x <1' then f-(]2,4[) is %3D O None of the choices O 11,2[ andfis continuous O 1.2 and fis not continuous O 11.2] and fis not continuous

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: dt converges. There is no value of r such that (3t)-" 14.

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Q: Show the uniformly converge to F Fn CX) = X 12 Fn (X)= X 1X€ (-10] XER %3D

A: We know that if a sequence of function has bounded derivative the uniformly convergent

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A: Let us consider the function fn(x)=xn on [0,1]. Let u assume that the function fn(x)=xn is pointwise…

Q: If n = 18, then the interval of the form (- t(n-1), alpha/2 , t(n-1), alpha/2), that contains 99% of…

A: From the given information, number of observations n = 18. Confidence level  Level of significance

Q: 4. At x = 4, the function f(x): (x², x ≤ 4₁ = is (4x, x>4 A. continuous but not differentiable B.…

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Q: @) 2) Fs of (x) = -PFC (Psy) -} [ If f (x,y) → as 6004X proof. (H-w.) then в

A: Introduction: The Fourier sine and cosine transforms are variations of the Fourier rework that do…

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Q: expand f(z) =1/z2 in power of z+1

A: I hqve used binomial expansion

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Q: Let fn (æ) = a" – x2", defined on [0, 1] %3D is pointwise converges to f (x) = 0, on [0, 1] then ||…

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Q: Expand f(z) =1/z2 in power of z+1

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Q: 2. Show that X H→ In x is increasing on (0,0) and that In 1 = 0:

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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

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A: Evaluate the given function  as follows.

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A: Given that, f is a continuous function on [0,∞). And, ∫3∞f(x)dx  converges. Then,…

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Q: (x-1) The following improper integral ; (x+1)(x²-x+1) converges to 2ln (4)

A: Improper integral.

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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…

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A: Given, the series ∑an diverges, then we have to find the values of c for which the series ∑can…

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Q: 11. Suppose f and g are continuous positive functions. Provide an example such that diverges and…

A: We need to provide example for convergence.

Q: If f has critical number at x=2, then f(2) is extreme value True O False

A: Explanation of the answer is as follows

Q: Expand f(z)=1/z2 in power of z+1

A:

Q: 4. Consider the sequence of functions {fn}=2 where fn: [a, b] R defined for n > 2 by if 0 < x <- fn…

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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: 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: Determine the GINI Index of Country X whose Lorenz curve is f(x) =;x² +÷x*. If Country Z 3 has a…

A: The Lorenz curve  of country X is f(x)=12x2+12x4. The GINI index  of a certain country with Lorenz…

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…

A:

Q: 4. Find two values of c in [-4, 4] such that f(c) is equal to the average value of f (x) = 3 cos 2x…

A: To determine c such that f© is equal to the average value of f(x).

Q: a) is f(x) = x3sin(1/x) uniformly continuous at (0,2] b) is g(x) = ln(x2+2) uniformly continuous at…

A: Solution a: Given f(x)=x3sin(1/x) at (0, 2] Since the given function is continuous at (0, 2] and…

Q: Suppose f'(x) = 0 wheneverx - a and x = b. Also, f'(x) does not exist whenever x = C. Then a, b and…

A: We will find out the required solution.

Q: 2. Sketch the graph of one function g that is continuous on [-4, 4] and has all of the following…

A: Solved below.

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A: Given problem is :

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Q: The critical Points of f (x, y) = x³ - 3x +3y2 -6y are: O (-1,1) and (1,1) O (1,1) and (1,1) O None…

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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: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

A:

Q: Suppose f and g are continuous functions. Provide an example such that | g(x)dr diverges 0. adf(x)dr…

A: Follow next step

Q: 4. Letf(x)=x22/5 - 19x². Determine the largest n for which fis n-times continuously differentiable.

A:

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: x2/3 is (are) The critical number(s) of f(x x – 1

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Q: The sequence of functions fn : x → x" sin(x" +2) + x 1. converges pointwisely to x over (0, 1/4] but…

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Q: Expand f(z) =1/z2 in power of z+1.

A: Taylor series of function f(x) about x=a is defined as:             f(x)=f(a)+f′(a)…

Q: 9. Consider the following continuous function: %3D defined on the closed, bounded interval [-8, 8].…

A: Given function:

Q: Define the sequence of functions {fn(x)} on [0, 1] by { 2n2x; 2n(1 — пх); т. fn(x) : 0; n Find f(x)…

A: