If the Taylor series expansion of a function f(x) =In(1+x)about the point x 1 is (x-1) (x-1)² Inx In2+ then the value of a is +.. %3D a 8. a) 2 b) -2 c) (p none of these O b) CO a) EO d)

Q: Find the Taylor series in (x – a) through (x – a)³ for f(z) = 2 – z + 3z2 – 2°, a = -1 f(x) = (x +…

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Q: 21a Determine the Taylor series generated by the function f(x) = 6sinx about the point a = (-1)" ·…

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Q: Compute the Taylor series of the function around x = 1. f(x) - ебх f(x) = = E( (6)"(.º)(x – 1)" +1…

A: Consider the function  Compute Taylor series of the function about x=1

Q: Compute the Taylor series of the function around x = 1. f(x) = e6x *( (6)"(x – 1)"+1 ) tx)-Σ f(x) n…

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Q: In the Taylor series expansion of exp(x) + sin (x) about the point x = T, the coefficient of (x- T)2…

A: The given function is f(x) = ex + sin(x) we have to find taylor series expansion about x = pi.

Q: The fourth nonzero term of the Taylor series expansion of In(x+4) centered at x =-3 is a) 글(+3)…

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Q: 20) The Taylor series for the function F(x) = S e¯ dt is E(-1)"n(4n+1) z4n+1 all x E R. n=0 a) True…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the Taylor series generated by f at x = a. 1 ,a = 6 9 - x f(x) (x – 6}n Σ (х - буп n=0 3n 3n+1…

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Q: Find the Taylor series generated by f at x = a. 4 f(x) = , a=D1 %3D O A. 4 E (-1)"(n + 1)x" n 0 O B.…

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Q: Find the Taylor series for f centered at c = 3 if f(3) = 4 and f'(x) has a Taylor expansion (х — 3)"…

A: Given  f'(x)=∑n=1∞x−3nnf(3)=4

Q: Find the Taylor series generated by f at x = a. f(x) = e 3×, a = 9 * e27 3n (x - 9)n Σ n! n=0 e27…

A: Given: f(x)=e3x,  a=9

Q: Find the first three nonzero terms in the Taylor Series of f about z a if S(r) = cos(2r), a =

A: To find  The first three nonzero terms ion the Taylor series of f about x=a.

Q: Find the Taylor series generated by f at x = a. 1 f(x) ', a = 6 9 - x (x – 6n Σ 3n+1 Σ (x – 6}n+1…

A: The given function is:  f(x) = 1/(9-x)

Q: Find the Taylor series generated by f at x= a. f(x) = -, 1 a = 3 X (x- 3)" Ο Α Σ 3" OA. n =0 (x –…

A: We have to find the Taylor's series for given function at a=3 . For this all order derivatives of f…

Q: Prove that the Taylor series around a = 0 for f(2) = e-2= converges to f(r) for all z € R.

A: To prove that the Taylor series around a=0 for fx=e-2x converges to fx for all x∈R. f'x=-2e-2x…

Q: 41. Use the Taylor series generated by e* at x = a to show that (x – a)² e* = 1 + (x – a) + 2!

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Q: Derive the Taylor series expansion of f(x)= e-3 about a = = 1.

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Q: Find the Taylor series generated by x = a for the following functions 1) f(x)= x'- 2x + 4, a = 2…

A: Here I am attaching image so that you understand each and every step.

Q: Use substitution (as in Example 4) to find the Taylor series at x = 0 of the functions in Exercises…

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 13. Find the Taylor series generated by f at r = a and the Maclaurin series: (a) f(x) = 1/x², a = 1…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

Q: (s) If the Taylor series of a function f (x) is 2n(n + 1) n=1 (a) identify Cn- (b) find f(4) (0).

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Q: Prove that the Taylor series around a = 0 for f(x) = e=2ª all x E R. converges to f (x) for

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Q: Which of the following is the Taylor series representation of f(x) = sinx centered at a = 1/2? O a.…

A: Because Here a = π/2 So I am Providing direct Answer y=∑n=0∞-1n2n!x-π22n

Q: Find the first three nonzero terms in the Taylor Series of f about r = a if S(x) = (x +1)°, a = 2

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Q: If f(x) = then the Taylor series for f(x) at a = 1 is: %3D 1+2x En-o(-1)"_2" B) o (x – 1)". C) E…

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Q: Determine the Taylor series of the function f (x) = (3+ x) around r = 1. a) (-1)"4"(z – 1)" 6) Č…

A: SOLUTION-

Q: In the Taylor series expansion of exp(x) + sin (x) about the point x = T, the coefficient of (x-7)2…

A: We will find out the required value.

Q: Use the Taylor series expansion of the function cosx about a = 0 to determine that of the function f…

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Q: Determine the Taylor series of the function f (α) - (5+ ) around x 1. α) Σ-1 16-"-1 (z - 1) b) Ž…

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Q: Determine the 8th term of the Taylor series expansion of f (x): %3D 1+r at a = 1 (-1) 256 (z-1)* 128…

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Q: 3 Let f(2)= (2 + 1)(x - 2) and use this result to evaluate Find the Laurent series expansion of f…

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Q: What are the first terms of the Taylor series generated by f(x)= at x=2? 1 22 (x-2), (x-2) (x-2)…

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Q: find the Taylor series at x = 0 of the functions in Exercises 1–2. 1.ln(3+6x) 2. 5sin ( -x)

A: Consider the given question,(1)The Taylor series at x = 0 is given by,

Q: In the Taylor series expansion of exp(x) + sin (x) about the point x = a, the coefficient of (x -…

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Q: The Taylor series of the function f(¤) = e=*+4z-2 centered at zo = -2 is given by %3D Select one: 00…

A: Taylor series of a function is the sum of infinite terms.

Q: In Exercises 41 and 42, let f()) = sin x. 42. Multiple Choice Which of the following is the Taylor…

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Q: Find the Taylor Series representation of the function f(x) = In(ax+b) Then evaluate the first three…

A: Note: It is assumed the expansion is asked about the point x=0 and the series evaluation is to be…

Q: Find the Taylor series generated by f at x = a. 1 f(x) = -, a =5 X (- 1)"(x- 5)" O A. E 5h + 1 n = 0…

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Q: Find the Taylor series generated by f at x = a. f(x) = cos (2x + 2r), a = 3r / 4 ..... Choose the…

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Q: Give the Taylor series expansion of f(x) = e^−3x^2+2 about a = 1. Approximate e^2 using the first 5…

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Q: 3. Find the Taylor series of f(x) at the given value.. X £.(x)... b. f(x) = cox az ..A=... a. C. X…

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Q: Obtain the Taylor series ez = e Σ [(z - 1)^n / n!]     (|z - 1| < ∞) for the function f(z) = ez…

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Q: What is the Taylor series of f(x)=-(1/x^2) which is centred at b=2?

A: The Taylor series is written as     ∑n=0∞fn(a)n!(x-a)n So, we will have to take n derivatives of…

Q: Which of the following is the Taylor series expansion of the function f(x) =e-2 with center a 2n n!…

A: Given function is f(x) = e-x2

Q: Find the Taylor Series representation of the function f(x) = In(ax+b) Then evaluate the first three…

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Q: The coefficient of r in the Macularin series of (e-1) sin r is 1 A. В. 4! С. 3! D. -1 Е. О F. 1

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Q: Find the taylor Series of f(x) centered at the given valve of a and the interval on which the…

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Q: find the Taylor series at x = 0 of the functions in Exercises 1–5. 1. e^-5x 2. sin ( paix/ 2) 3. ln…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.