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Worksheet 1. What is the difference between a Taylor series, a Maclaurin series, and a power series? 2. Find the Maclaurin series for f(x) = 3x² cos(5x). 3. Find the Maclaurin series for the derivative of 3x² cos(5x). (Hint: Use the answer above and find the deriviative of the series for 3x² cos(5x).) 4. Find the Maclaurin series for f 3x² cos(5x) dx. 5. Find the first 3 terms of the Maclaurin series for f(x) = √√√x +4. 6. Find the first 4 terms of the Taylor series for f(x) = x ln x centered about a = 2. 7. If f(x): = k=0 5k k! xk, what is f"(0)? Page 2