This** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
This** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
This** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**Unformatted text preview: **X n =1 (-1) n +1 ( n √ e-1) 2. (10 points) Find the second-order 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 ( x-4) 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 (1-cos 2 x ) e x 3-1 (b) lim x →∞ x 2 ± e-1 /x 2-1 ²...

View
Full Document

- Fall '07
- Nelson
- Calculus, Power Series, Taylor Series, Mathematical Series, #