Maclaurin series by substitution practice problems
Maclaurin series built from known ones by substitution and multiplication. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Use a known Maclaurin series to find the first four nonzero terms of the Maclaurin series of \( \displaystyle f(x) = - x + e^{x} - 1 \).
Use a known Maclaurin series to find the first four nonzero terms of the Maclaurin series of \( \displaystyle f(x) = x^{2} \sin{\left(x \right)} \).
Use a known Maclaurin series to find the first four nonzero terms of the Maclaurin series of \( \displaystyle f(x) = \frac{\sin{\left(x \right)}}{x} \).
Use a known Maclaurin series to find the first four nonzero terms of the Maclaurin series of \( \displaystyle f(x) = \frac{1}{1 - x^{3}} \).
Use a known Maclaurin series to find the first four nonzero terms of the Maclaurin series of \( \displaystyle f(x) = e^{- x^{2}} \).
Use a known Maclaurin series to find the first four nonzero terms of the Maclaurin series of \( \displaystyle f(x) = \frac{\sin{\left(2 x \right)}}{x} \).
Use a known Maclaurin series to find the first four nonzero terms of the Maclaurin series of \( \displaystyle f(x) = x \cos{\left(x \right)} \).
Use a known Maclaurin series to find the first four nonzero terms of the Maclaurin series of \( \displaystyle f(x) = \ln{\left(2 x + 1 \right)} \).
Use a known Maclaurin series to find the first four nonzero terms of the Maclaurin series of \( \displaystyle f(x) = \ln{\left(x + 1 \right)} \).
Use a known Maclaurin series to find the first four nonzero terms of the Maclaurin series of \( \displaystyle f(x) = \cos{\left(x^{2} \right)} \).