Math 106 A and B ←− circle your section Quiz 06 page 1 03/02/12 Name
1. Let f(x) = x4/3=3
√x4. You do not need to verify this, but in powers of (x−1), the second degree Taylor polynomial
for f(x) is P2(x) = 1 + 4
3(x−1) + 2
9(x−1)2, and f(3)(x) = −8
27 x−5/3.
(1A) On the interval (0.9, 1.2), what is the error guarantee for this polynomial? Show all your work, including the “error
guarantee formula”.
(1B) What is the actual error at x= 0.9 (show how you found it).
2. Consider the improper integral Z∞
12
(x+ 13)−3/2dx.
(2A) Show that it converges, and find out to what. As we’ve done in class, make a table using at least four well-chosen B
values that obviously supports your conclusion. Use goo d notation throughout, including the limit process involved.
(2B) BONUS: Find Bto several digits for which ZB
12
(x+ 13)−3/2dx gives 99.9% of the area represented by the integral
in (2A).
