Unformatted text preview: , 3 / 2] is at most 103 ? What if the interval is instead [1 , 3 / 2]? ⇒ 3. Find the ﬁrst three nonzero terms in the Taylor series for tan x on [π/ 4 , π/ 4], and compute the guaranteed error term as given by Taylor’s theorem. (You may want to use Maple or a similar aid.) ⇒ 4. Show that cos x is equal to its Taylor series for all x by showing that the limit of the error term is zero, as N approaches inﬁnity. 5. Show that e x is equal to its Taylor series for all x by showing that the limit of the error term is zero, as N approaches inﬁnity. 10.12 Additional exercises These problems require the techniques of this chapter, and are in no particular order. Some problems may be done in more than one way....
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 Fall '07
 JonathanRogawski
 Math, Calculus, Addition, Approximation, Taylor Series, Natural logarithm, Additional Exercises, polynomial approximation

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