Prove using the e-8 notation that the following functions are continuous at p= 1: (a) g2(r) = 2=+7 2+7 %3D (b) g2(x) = %3D I+7

Q: Find c such that the function 10 г c - || 26 х > с is continuous everywhere. c =

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Q: 8. If g(x) = e*In(x+1), compute g'(x). What techniques are you using in this case?

A: Solution is given below..

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Q: Let f(t) be continuous for all 120 and be of exponential order as t o and if

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Q: Find conditions on a and b that ensure f (x) = x3 + ax + b is increasing on (−∞,∞).

A: Consider the given function as fx=x3+ax+b

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Q: FInd the deriviative of the following functions with respect to x by using the chain rule.  (a)…

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Q: Find a constant c such that x² – c2 if x 4 g(x) ={ is continuous everywhere.

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Q: 23 Find a positive value c, for x, that satisfies the conclusion of the Mean Value Theorem for…

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Q: If f(x) is a continuous function on [3,7] and F(x) is an anti-derivative of f(x) such that F(3)=7…

A: Given :f(x) is continuous function 3,7Fx is anti-derivative of fxF3=7 and F7=3To determine…

Q: LET F(X) =2 x SIN(X), AND EPSILON = 2 × 10-7. FIND OPTIMUM STEP VALUE THAT CAN BE USED WITH CENTRAL-…

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Q: The function g(x) = ln(x³ – 1) defined on V2, 0) is not zero unless x 2.

A: Given statement

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 g(x) be a continuous function and let g(") (x) be the n-th derivative of g(x). Find an example…

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Q: Find the anti-derivative of g(x) = 2*, which contains the point (0, 2.44). ⒸG(x) = -2 O G(x) = 2 O…

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Q: Find all a E Z such that f(x) =

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Q: Prove that for the gamma function [(x) = ftx-¹e-tdt that for n a positive integer then I(n) = (n-1)!

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Q: Decide whether or not the real function In (eon 2) I+0, = (1) 1= 0, is continuous at r = 0.

A: The given function is fx=ln cos2x2x2     if  x≠0-1                if  x=0. Compute the limit…

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: iii. Does there exist a function x e X such that 50) = f + [ e*: e x(s) ds x(1) = 1² for every t e…

A: It is given that X=C0,1 with the following norm, x=maxt∈0,1 xt The map T:X→X defined as follows:…

Q: Find the value(s) of k that makes the function continuous over the given interval. a < k k < a S 3x…

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

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Q: Suppose f(x) has the following properties: f(x) is continuous and positive for all a E [3, 19] f(x)…

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Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

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Q: 1. Apply the Parseval's identity to the function f (x) = x, –n < x < n

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Q: . Find a value of k so that the following function is continuous at x = 1. f(x)%3D x<1 x-1 2kx, x21

A: Given: The given function                                             To find: The value of k, such…

Q: A continuous X Co F(x1= ++x o BX C1 K 1 ≤X Find value of k V-V- X has CDF 16 17 18 19 20 21

A: Given CDF is F(X) = 0,x&lt;012x,0≤x&lt;1k,1≤x

Q: 4) Find the value of the constant k so that the function (1 – k, if z<3, f(z) = 1– kr, if 123, is…

A: This question is related to limit and continuity of a function, we will use condition for a function…

Q: Let f(x) be piecewise continuous and a -exponential. In this case, prove that F(s) L £{f(x)} = F(s)…

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Q: Determine the value of k so that the following is a pdf. f(x) = k(1 + 2x) for 0 < x < 2

A: From the definition : The function f is probability density function of a random variable x in the…

Q: Man of X = Avenge f= ELK) H.w prove that E (x-x) =0 Hint 又=E(x)

A: to prove EX-X=0 using the property of Expectation  EX+Y=EX+EY therefore, EX-X=EX-EX now let Xi be a…

Q: The table below shows the average rates of change for points near In (2) for the function f(x) = e +…

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Q: let a function f(x) be given by f(x) = log(r +x) prove that f log(e+x) (x)is decreasing on [0,0]| ]

A: The solution for the above question is as shown below.

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: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b -1<x<1, 3 x21 Continuous at x=0

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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: b) Let f(x) = ¹. Find f'(x), ƒ"(x), ƒ"(x) and ƒ(4) (x). Deduce f(n)(x).

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Q: LET F(X)=1/X.USE CENTRAL- DIFFERENCE FORMULA FOR F '(X) OF ORDER O(H4 ) WITH STEP SIZE H = 0.1 TO…

A: Given that fx=1x Step size h=0.1 To find f'2: Central difference formula for f'x of order Oh4:…

Q: Find the Wronskian for the set of functions.{e−x, xe−x, (x + 3)e−x}

A: To Find theWronskianfor the set of functions. {e-x,xe-x,(x+3)e-x}

Q: Let x~ possion(alpha). Show that E[x(x-1)(x-2)....(x-k)]=ak+1

A: Solution

Q: øz (@) is a continuous function of o in the range -o < @< ∞.

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Q: Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval.…

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Q: The Wronskian of the given function (e2x, e*/2 ) is 5x 3 e z

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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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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.