This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: X n =1 (1) n +1 ( n √ e1) 2. (10 points) Find the secondorder Taylor polynomial of the function f ( x ) = 3 √ x near x = 8. Compute the approximate value of 3 √ 10 given by this polynomial. (Leave your answer in fraction form, but simplify it.) 3. (8 points) For which values of x does the power series ∞ X n =2 ( x4) n n ln 2 n converge? Justify your answer. 4. (10 points) (a) State (or compute) the Taylor series centered at 0 of f ( x ) = ln(1 + x ). (b) State (or compute) the Taylor series centered at 0 of g ( x ) = 1 1 + x 2 . (c) Compute the ﬁrst four nonzero terms of the Taylor series centered at 0 of h ( x ) = ln(1 + x ) 1 + x 2 . 5. (10 points) Compute the following limits: (a) lim x → sin 3 x (1cos 2 x ) e x 31 (b) lim x →∞ x 2 ± e1 /x 21 ²...
View
Full Document
 Fall '07
 Nelson
 Calculus, Power Series, Taylor Series, Mathematical Series, #

Click to edit the document details