Find the Taylor polynomial T3 (x) for e^3x centered at 0. What is T3 (1)?  (T3 is suppose to look like the image I posted below but i didn't know how to type it.)

Q: How would I use those non-zero terms and make

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Q: Consider the Lagrange polynomial that passes through the 4 data points given by 2 8 y 7 | 151 | 407…

A: We know that L0x is given by  L0x=x-x1x-x2x-x3x0-x1x0-x2x0-x3        1 Here, x0=2,x1=5,x2=7,x3=8,x=4…

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A: The remainder term R2(x) = f(x) - P2(x), for second degree taylors polynomial.

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Q: Calculate the Taylor polynomials T2 and T3 centered at x = a for the function f(x) = In(x + 1), a =…

A: Given function is  fx=lnx+1. To calculate Taylor polynomials T2 and T3 centered at x=a, we write…

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A: ∫xndx = xn+1n+1+C