MAT 21B
wksht2

# wksht2 - ESP Kouba Worksheet 2 1 Evaluate the following...

• Notes
• 2

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.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ESP Kouba Worksheet 2 1. Evaluate the following sums. 300 oZoo a. ’21: b. 2(31-2) Lil g:i 00 [000 c. .52(5i2-i+1) d. ,Z(i+1)i L31 (.1! e34 203 e. Z(i—1)2 r.. [(i+1)3—i3] {:233 L31 2. Estimate the area of the region between the graphs of y = e X and y = J? over the interval [0, 4]. Use rectangles determined by the midpoints of four equal subdivisions. 3. Estimate the volume of a hemisphere of radius four feet. Use appropriate cylinders determined by the midpoints of tour equal subdivisions. 4. Use rectangles to estimate the area below the graph of f(x) = in x and above the interval [1, e 2]. Let the partition of [1, e 2] be x 0 =1, x1 =2, x2=2.6, x3=4, x4=6.5,and x5=e2. Lettherectanglesbe determined by the sampling points 01 = 3/2, c 2 = 2.1 , c 3 = 3 , 04:6,and c5=6.9. Y1 5. Evaluate Z t( c i) (xi — Xi_1) for each of the following. L:l a. t(x)=lnx on [1,e2] partition: XO=1 , x1 =3, x2=6, X3=e2 sampling points : c i is midpoint of subdivision [X H, x i] tori: 1,2,3. b. f(x)=e><2 on [4,1] partition1XO=-1,X1=—1/2,x2=0,x3=1/2,x4=1 sampling points: ci=xi for i=1,2,3,4 0. f(x) = tan x on [qt/4, 0] partition: x0=—1t/4, x1=-1c/6, x2=-1t/12, X3 =0 Sampling Poih‘ks -. CL:X£_, \$ov~ L: 11.2)} 6. Use rectangles, determined by the right-hand endpoint of n equal subintervals, to estimate the area under the graph of y = 1/2 x 2 + x above the interval [0, 4]. a. n=2 b. n=4 c. n=20 d. n=100 e. What is the limit of the estimates as n approaches infinity ? DEFINITION : The definite integral of f over the interval [a, b] is b V] lt(x)dx= lim Zf(ci)(xi-Xi_1). a mesh—>06l 7. Determine the mesh of each of the following intervals and partitions. a. [0, 2], partitioned into ten equal subdivisions b. [—4, 2], partitioned into five equal subdivisions 0. [—3, 2], partition: x0=-3, x1 :26, xl=—1 , x3 =0, = 1. x 8, 5:2. “I 8. Use equal subintervals and the limit definition of a definite integral to evaluate each of the following. i a. i7dx O .1 b. i(3x—l)dx ...
View Full Document

• Spring '07
• MAT21B
• equal subdivisions, Lil g

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern