This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ESP Kouba
Worksheet 3 1. Assume thatf is a function satisfying f '(x) > 0 for all values of x in
the interval [a, b]. Let [a, b] be partitioned by a =x 0 < x1 < x2 < < x n = b . Determine which of the following quantities is largest, or
state that it is not possible to determine. Vl Vt ‘ Xi‘1)and .Z " Xi_1) (it (:1 2. Use equal subdivisions and the limit definition of a definite integral to
evaluate each of the following. lo 10
a. [1:3 dx b. Jx3 dx
I 1 3. Assume that a thin rod lies along the interval [a, b] and has density f(x) grams per centimeter at pointx . Let x 0, x1 , x 2 , . . ., x n be a
partiton of [a, b] and c1 , c 2, c 3 , . . . , c n corresponding sampling
numberswith ci in [xi,1, xi] for i=1,2,3,...,n. Whatisthe physical interpretation of each of the following quatities ? a. Xi'Xi_1 b‘ n
C. f(Ci)(XiXi_1) I f(Ci)(Xi'Xi_1)
at
n h b
e. lim .2f(ci)(xixi_1) f. Jf(x)dx
mesh*0 5' a
b 4. Each of the following limits is equal to a definite integral J f(x) dx .
Determine the definite integral for each. a in
3. lim ’Esin(i/n)1/n “+00 133 V\
b. Iim '2 sin(3 + i/n)1/n “+00 L=
32"l
I. El” W) 3
c. rm . ’ —~
haw all W
V\
. Ll
d. lrm 2, +14.
“900 C! 3n L 5. Let f be a function which is differentiable for all values of x. In
addition, the function satisfies f'(x) = 5 f(x) for all values of x. Show
that there exists at least one number 0 satisfying 10 f(c) = f(3)  f(1) ...
View
Full
Document
This note was uploaded on 12/01/2010 for the course MAT 21B MAT 21B taught by Professor Mat21b during the Winter '07 term at UC Davis.
 Winter '07
 MAT21B

Click to edit the document details