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Consider the function f(x)=e−x2.
Find the first three non-zero terms in the Maclaurin series for f(x).
Hence find an approximation for the value of e−0.01, giving your answer to four significant figures.
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In small-angle modeling (e.g., pendulum motion), the Maclaurin series for cosx is often used to approximate cosθ where θ is measured in radians and is close to zero.
Write down the first four non-zero terms of the Maclaurin series for cosx.
Use your result from part (a) to estimate cos(0.3) correct to 4 significant figures.