1. Find a power series representation for the function f(x)= 5^x

2. Find the coefficient ofx^6in the Taylor series expansion centered atx= 0 for f(x) = 5ln(73x^2)

1.coefficient ofx6= 90/343

2.coefficient ofx6= 135/1372

3.coefficient of x6= 45/686

4.coefficient ofx6= 45/343

5. coefficient of x6= 135/686

3. Find a power series representation for 4 + 2x/1+x

Hint:separate then use the series for 1/1+x.

4. Find a power series representation for the function

f(x)= x/ 9x+1

5. Find a power series representation for the

function f(x)= ln (sqrt (1+2x/1-2x) )

(Hint: remember properties of logs.)