Solutions Exam 1

# Solutions Exam 1 - Version 069 – Exam 1 – gualdani...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Version 069 – Exam 1 – gualdani – (57180) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points At which point on the graph U T S R Q P is the slope greatest ( i.e. , most positive)? 1. S correct 2. U 3. P 4. T 5. Q 6. R Explanation: By inspection the point is S . 002 10.0 points If a ball is thrown into the air with a velocity of 50 ft/sec, its height in feet after t seconds is given by y = 50 t − 16 t 2 . Find the average velocity of the ball for the time period beginning at t = 1 and lasting 1 / 4 seconds. 1. average vel. = 11 ft/sec 2. average vel. = 13 ft/sec 3. average vel. = 10 ft/sec 4. average vel. = 12 ft/sec 5. average vel. = 14 ft/sec correct Explanation: If the height of the ball after t seconds is given by y = y ( t ) = 50 t − 16 t 2 , then the average velocity of the ball over a time interval [1 , t + h ] is avg. vel. = y (1 + h ) − y (1) h . Now y (1 + h ) = 50(1 + h ) − 16(1 + h ) 2 = 50(1 + h ) − 16(1 + 2 h + h 2 ) = 34 + 18 h − 16 h 2 , while y (1) = 50 − 16 = 34 . Thus y (1 + h ) − y (1) h = 18 h − 16 h 2 h = 18 − 16 h. Consequently, when h = 1 / 4, therefore, average velocity = 14 ft/sec . 003 10.0 points Below is the graph of a function f . Version 069 – Exam 1 – gualdani – (57180) 2 2 4 6 − 2 − 4 − 6 2 4 6 8 − 2 − 4 Use the graph to determine lim x → 4 f ( x ) . 1. limit = 6 2. limit does not exist correct 3. limit = 9 4. limit = 18 5. limit = 4 Explanation: From the graph it is clear the f has a left hand limit at x = 4 which is equal to 4; and a right hand limit which is equal to 0. Since the two numbers do not coincide, the limit does not exist . 004 10.0 points If f oscillates faster and faster when x ap- proaches 0 as indicated by its graph determine which, if any, of L 1 : lim x → 0+ f ( x ) , L 2 : lim x → − f ( x ) exist. 1. neither L 1 nor L 2 exists 2. L 1 doesn’t exist, but L 2 does correct 3. L 1 exists, but L 2 doesn’t 4. both L 1 and L 2 exist Explanation: For x > 0 the graph of f oscillates but the oscillations do not get smaller and smaller as x approaches 0; so L 1 does not exist. But for x < 0, the graph oscillates and the oscillations get smaller and smaller as x approaches 0; in fact, the oscillation goes to 0 as x approaches 0, so L 2 exists. Consequently, L 1 does not exist, but L 2 does . 005 10.0 points Determine lim x → 2 braceleftBig 1 x − 2 − 2 x 2 − 2 x bracerightBig ....
View Full Document

## This note was uploaded on 05/12/2010 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas.

### Page1 / 9

Solutions Exam 1 - Version 069 – Exam 1 – gualdani...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://www.coursehero.com/file/5890394/Solutions-Exam-1/", "fetch_time": 1495559802000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2017-22/segments/1495463607648.39/warc/CC-MAIN-20170523163634-20170523183634-00618.warc.gz", "warc_record_offset": 864778213, "warc_record_length": 24391, "token_count": 1039, "char_count": 3189, "score": 4.1875, "int_score": 4, "crawl": "CC-MAIN-2017-22", "snapshot_type": "longest", "language": "en", "language_score": 0.8296222686767578, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00015-of-00064.parquet"}