1. Given the series 2²-1 a) Define f(x) = Given the fact that z²+1=(2²+√√2x + 1)(x² -√√2+1) explain how can you find the anti-derivative by hand using partial frac- tional decomposition. (Just give the form, no computation required.)

Q: Given the function f(x)= rt(x) a) find the 3rd taylor polynomial at c=9. Write the coefficents as…

A: Given that: fx=x To find: (a) find the 3rd Taylor's polynomial at c=9. Write the coefficents as…

Q: Consider the falowing. (A computer algebra system is recommended.) t-(-9. 2s*. 4) -) (a) Sketch the…

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Q: Let p(x) be a polynomial that is divisible by (x-a)n where n∈ N and n >= 2. Prove that p'(x) is…

A: Here, given that the polynomial p(x) is divisible by (x-a)n. So, p(x)=(x-a)nq(x)...(1) Where, q(x)…

Q: Q2) Find the expansion in Legendre polynomials of the functions: a) f(x)=2-x-x² x) = { 1 ) 0, b)…

A: We have to find the expansion in Legendre polynomials of the function.

Q: Consider the function: f(x) = ln(r) Determine the quadratic Taylor Polynomial about the point zo =…

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Q: Let f: (-pi/2 , pi/2) -->R be given with f(t) = tan-1(t) What is taylors polynomial P1(t)  of the…

A: f(t)=tan-1(t),  f(0)=tan-1(0)=0first we find the derivative of f(t) f'(t)=11+t2f'(0)=11+0=1taylor…

Q: 2. Find the nested form Q(x) of the polynomial f (x) = 6cos' x– 2cos x+cos.x –1. Evaluate Q(1.5)…

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Q: Let P(x)=20x*-7x3 be the Lagrange interpolating polynomial that approximates a function f over the…

A: Given that P(x) approximates a function f over the interval -1, 1, where P(x)=20x4-7x3is the…

Q: Evaluate the improper intergal 1 dxusing the residue theorem. (x2 + 9)?

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Q: 2 4) + +2 +2

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Q: Find the interpolating polynomial of degree two for f(x) cos(r2) +r on the interval [-1, 1] using…

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Q: b) Used bisection method to find the root of f(x)= x³ + 3x-5, Do calculation until six iterations in…

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Q: Find (x³ + 2x²) dx using the Riemann sum.

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Q: (2) Construct the Simpson 3/8-th formula to approximate f(x)dr by using La- grange interpolating…

A: Given: ∫abf(x) dx and the function f(x), where the interval of integration a, b is divided into n=3…

Q: 1. Algebraically check if the following polynomial function has a point of symmetry at (0, 0) or a…

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Q: Evaluate the integral using substitution and then Integration by Parts: Leve = x ² ) dx (Hint: Let u…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Find the Chebyshev rational function approximation of the function f (x) = e=* in N =6 (m=3 and n=3)…

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Q: Below is a graph of function f(x). Which of the following could be the second Taylor polynomial of…

A: We have to find the Taylor second order polynomial.

Q: Find a monic polynomial of least degree in R[x] that has 1-i and 2i as roots.

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Q: Consider the following Polynomial f(x)= x- 3x-10x+x+2 Compute the root x=l of the above function…

A: (1) Given that f(x)=x4-3x3-10x2+x+2 To find the root of the equation by bisection method.

Q: Let f(x) =x/x + 1 and g(x) =2/x . (a) Find a formula for the composition (f . g)(x). Express the…

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Q: What is the sixth-order Taylor polynomial for f(x) =/1+2x² about xo = 0? (A) 1 + x² – 8 16 x6 (B) 1…

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

Q: Use the second Taylor polynomial P2(x)P2(x) for f(x)=x2+ln(1+x)f(x)=x2+ln⁡(1+x) about x0=0x0=0 and…

A: P2x=f0+f'0x-0+f''0x-02f(x)=x2+ln(1+x)f(0)=0f'(x)=2x+11+xf'(0)=1f"(x)=2-1(1+x)2f"(0)=2-1=1∴P2(x)=x+x2…

Q: 20. Find the splitting field for x^2-2sqrt(2)x+3 over Q(sqrt(2)). Find the roots first then…

A: To Find: Splitting field of x2-22x+3=0 over ℚ2.

Q: 1. Consider the function f(x) = x³ + 3x (a) Find the second Taylor polynomial T₂(x) for f(x) based…

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Q: Suppose a functions satisfies f(5) = 2, f'(5) = 5, f"(5) = -7, and f"(5) = 12. What is the third…

A: We need to find correct option.

Q: Use the nspire calculator to integrate (b) Use the shorteut formulas to find L{81* – 5t² –…

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Q: Which of the follow is the Least Common Denominator of the rational expressions below 4z and -3 I+7…

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