Question

Problems: Find a power series representation for the following functions and determine the interval of convergence: 1) f(x) = 4 / (2x + 3) 2) s(t) = t / (2t^2 + 1) 3) y(w) = ln(5 - w) Evaluate the following integral using a power series – what is the radius of convergence of the resultant anti-derivative? 4) ? t / (1 + t) dt 5) ? x^2 ln(1 + x) dx Use the definition of a Taylor Series to find the first four nonzero terms of the series for each of the following functions centered at the given value of a. Verify your result by graphing the function and the first four terms together. 6) G(r) = x exp[r]; a = 0 7) f(x) = ? x; a = 8 8) T(?) = sin(?); a = ?/6 9) ln(x); a = 2 Find the Maclaurin Series for the following functions using the definition of a Maclaurin Series (Taylor Series centered at 0). 10) f(x) = 2^x 11) f(x) = x cos x 12) f(x) = exp[-2x] 13) f(x) = tan^-1(x^2) 14) f(x) = exp[3x] - exp[2x] 15) f(x) = x / ?(4 + x^2)

          Problems:

Find a power series representation for the following functions and determine the interval of convergence:

1) f(x) = 4 / (2x + 3)
2) s(t) = t / (2t^2 + 1)
3) y(w) = ln(5 - w)

Evaluate the following integral using a power series – what is the radius of convergence of the resultant anti-derivative?

4) ? t / (1 + t) dt
5) ? x^2 ln(1 + x) dx

Use the definition of a Taylor Series to find the first four nonzero terms of the series for each of the following functions centered at the given value of a. Verify your result by graphing the function and the first four terms together.

6) G(r) = x exp[r]; a = 0
7) f(x) = ? x; a = 8
8) T(?) = sin(?); a = ?/6
9) ln(x); a = 2

Find the Maclaurin Series for the following functions using the definition of a Maclaurin Series (Taylor Series centered at 0).

10) f(x) = 2^x
11) f(x) = x cos x
12) f(x) = exp[-2x]
13) f(x) = tan^-1(x^2)
14) f(x) = exp[3x] - exp[2x]
15) f(x) = x / ?(4 + x^2)

Problems:

Find a power series representation for the following functions and determine the interval of convergence:

1) f(x) = 4 / (2x + 3)
2) s(t) = t / (2t^2 + 1)
3) y(w) = ln(5 - w)

Evaluate the following integral using a power series – what is the radius of convergence of the resultant anti-derivative?

4) ? t / (1 + t) dt
5) ? x^2 ln(1 + x) dx

Use the definition of a Taylor Series to find the first four nonzero terms of the series for each of the following functions centered at the given value of a. Verify your result by graphing the function and the first four terms together.

6) G(r) = x exp[r]; a = 0
7) f(x) = ? x; a = 8
8) T(?) = sin(?); a = ?/6
9) ln(x); a = 2

Find the Maclaurin Series for the following functions using the definition of a Maclaurin Series (Taylor Series centered at 0).

10) f(x) = 2^x
11) f(x) = x cos x
12) f(x) = exp[-2x]
13) f(x) = tan^-1(x^2)
14) f(x) = exp[3x] - exp[2x]
15) f(x) = x / ?(4 + x^2)

Added by Rodrigo M.

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