Practice Test 1
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1a. Find the nth Taylor polynomial for f(x) = (1 + 4x) − 3 around x=0.
1b. Let f(x) = cos(2x). Find an upper bound for R n(x) for −2 ≤ x ≤ 2. Show that
lim n→∞ R nx) = 0 for all x in this region. Find the Taylor series of this function
about x = 0.
2. Compute the foxlo−xng limits if they exit.
(a) lim e −e .
x→0 sin x