9. Given the Mac expansion of y = In(1+ x) below, use it to approximate In(0.4) to the 4th decimal place accuracy. What's the degree of the polynomial needed? In(1 + x) = £(-1)~-" 4

Q: To evaluate the exact value of f(x) = (4x5 + 7x-9)(x8- 3)2), how many terms of the Taylor series…

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Q: 2. Find the exact value of the term containing x" in the expansion of (x-3y)" using the Binomial…

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Q: nsion of φ(x) = 1/(1−x)

A: The given expression is φ=1(1-x), when n=4 and x0=-1

Q: What function represented by the following Taylor series * 1-+ x6 +.... at a= 720 x2 x4 2 24

A: The given series is: 1-x22+x424-x6720+......

Q: Find the coefficient of x* in the power series 3x² +2x expansion of (x +2)(x-3) |

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Q: Does the Taylor Series Expansion of f(x)=(1+3x)^(24) about a=1 have only a finite number of terms?…

A: To explain if the Taylor series expansion of f(x)=(1+3x)24 about a=1 have only finite number of…

Q: Evaluate the given function by using three terms of the appropriate Taylor series. √√4.3

A: Given: 4.3 To evaluate: The given function by using three terms of appropriate Taylor series.

Q: 1+2x Expand ()* in ascending powers of x up to and including the term in x³. B, 1 assuming x =…

A: Given : [(1 + 2x)/(1 - x)]⅓

Q: The Taylor expansion of In(1 + x)/x is given by (-1)" -z". n+1 3 n=0 Use the fourth-order Taylor…

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Q: c) Use Taylor series expansion of f(x) = In(1 + cos x) given by 1 f(x) = In 2-x²- *** 1440 to…

A: c Given that the Taylor series expansion of the function fx=ln1+cosx is given by…

Q: 4. Use the fact that the Taylor series for g(x) = sin(x²) is x6 x14 - - 3! 5! 7! to find g"(0),…

A: The function g(x) is given as  g(x)=sin(x2) Taylor series for g(x)=x2-x63!+x105!-x147!-------

Q: What is the Taylor's expansion of (3/x^4) about x=1 up to the first five non-zero terms?

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Q: Find the Taylor expansion of e−2x/3 around x = 0, write at least five terms.

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Q: Q/ Drive the Taylor series for: (X — 1). е* пеar X = 1

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Q: 5. Write down T2 (x), T4 (x) and T, (x) for the Taylor Series of f (x) = v2+x about x = 1. Graph all…

A: Given fx=2+x Taylor series at a is: fa+f'a1!x-a+f''a2!x-a2+.... Therefore,…

Q: 9. Given the Mac expansion of y = In(1+ x) below, use it to approximate In(0.4) to the 4th decimal…

A: To approximate ln(0.4) to the 4th decimal place accuracy using the Maclaurin expansion of y=ln1+x.

Q: Q/ Drive the Taylor series for: (X — 1). еx пear X3D 1 |

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Q: Q/ Drive the Taylor series for: (X — 1).е* пеar X3D 1

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Q: 3. Use Taylor Series manipulations to provide a Taylor polynomial of degree 5 for y = xços(2x)

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Q: 5. Find the Taylor expansion of f(x)=x² - 2x + 4 at x = 2.

A: To find the Taylor expansion of fx=x2-2x+4 at x=2.

Q: 4) Use the first three terms of the Taylor expansion for f(x) = eª to estimate e'/4. %3D

A: Okok

Q: ii. Compute f (x) = In(1 + 2x) at xị+1 = 1.1 by first, second, third, and fourth degree Taylor…

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Q: B. Find the first 4th terms for expansion of f(x)= In(1+3x) by using Mclaurin's Series.

A: We have to find ist four term

Q: Give the Taylor expansions of the 1st and 2nd order of f(x, y) in P= (-1, -1)

A: To calculate the Taylor expansions of 1st and 2nd order of f(x,y) at the point P=(-1,-1).…

Q: Write the taylor series cetered at c = 1 for f(x) = 3x

A: The Taylor series of function f(x) centered at x=a is given by: f(x)≈∑n=0∞f(n)(a)n!(x-a)n

Q: Does the Taylor Series Expansion of f(x)=(1+3x)^(24) about a=1 have only a finite number

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Q: Find the first 5 terms in the taylor expansion of e" resin(x) Plug in * and estimate ve in terms of…

A: Find the Taylor expansion of eSin(x) , then put x = (π/6) and calculate √e in terms of π.

Q: (14). . Find the first fuer terms of the Taylor Series for the function flx)= ex9 ○メ=o.

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Q: To evaluate the exact value of f(x) = x(8x49 - x)(x30 - 3) , what order of the Taylor series…

A: f(x) = x(8x49 - x) (x30 - 3)

Q: Compute the approximate value of In(2) using the Taylor polynomials calculated in (a). How large is…

A: Consider the function, f(x)=ln(x+1)  ⋯⋯(1) At x=0, equation (1) becomes, f(0)=ln(0+1)=ln1=0 Taking…

Q: Determine maximum error between 0.9 ≤ ? ≤ 1.1 interval for second degree Taylor expansion of ?(?) =…

A: find error

Q: 8.8.12. Use a known Taylor series to conjecture the value of the limit. 2x

A: The Taylor series of e^-2x can be obtained from that of e^x  as shown on board.

Q: 2 For n=1 a) Verify that that lin b₁=0. 7380 b) Compute Sy. <) Find an d) How малу Must be added Sum…

A: This is a multipart question having three or more interrelated subparts. As per the company policy,…

Q: Evaluate the given function by using three terms of the appropriate Taylor series. √16.2 √16.2=…

A: Consider a function f(x)=√x

Q: To evaluate the exact value of f(x) = (4x° + 7x - 9)(x29 - 3)29), what order of the Taylor series…

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Q: Under the same hypotheses as exercise 11, show that the Taylor expansion of f.g at 2o is obtained by…

A: We will prove the given statement.

Q: hlhat will be the Taylor Series oL In ! about x=0 up to and' Including the terms of order three?

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Q: in what way is a Riemann sum similar to a Taylor polynomial? (Other than the fact that both can be…

A: We have to write similarities between Riemann sum and Taylor Polynomial.

Q: 8.8.18. Use a known Taylor polynomial with n nonzero terms to estimate the value of the integral. n-…

A: Taylor series expansion is given on the White board. Since n = 4 , the approximation will be done…

Q: 2. Use the Binomial Theorem for the expansion of the function as a power ser: S(x) = V1+ 3x²

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Q: what is the nth order term in the taylor series expansion of f(x)= exp(x). about x= -3

A: Consider the provided question, The Taylor series expansion of f(x) is given as,

Q: f(x)=1/(3x+1), a=3

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Q: If we have the following Taylor series V7(x – 4)" | - f(a) Σ-1)" . n! n=0 f(7) (4)? what is

A: The given Taylor series is f(x) = ∑n=0∞(-1)nn(x-4)nn! We have to find the  f(7)(4)   f(x)…

Q: 6. Recall that In(1+ x) = x - + 4 for -1 <r < 1. ... 3 (a) Write out the first four nonzero terms of…

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Q: Find the binomial expansion of √(x² +1-y²) up to the fifth term.

A: As per the question we are given a bivariate function in variables x, y and we have to find its…

Q: Q4: drive the Taylor series for (х + 2)е* for х %3D —2 X =

A: The general form of the Taylor series expansion is…

Q: 3. Write down T2 (x), T3 (x) and T4 (x) for the Taylor Series of f (x) = In(1 – æ) about æ = -2.…

A: Given: fx=ln1-x To Find: i. T2x, T3x and T4x for the Taylor series of fx about x=-2.ii. Graph all of…

Q: Q/ Drive the Taylor series for: (X — 1). е* пеar X3D 1

A: