Elementary Technical Mathematics
11th Edition
ISBN: 9781285199191
Author: Dale Ewen, C. Robert Nelson
Publisher: Cengage Learning
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Chapter 6, Problem 15CR
To determine
To Calculate: The simplified form of the algebraic expression
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3) Let R be a set of real number and d:R2 R R such that
d((x, y), (z, w)) = √(x-2)² + (y-w)² show that d is a metric on R².H.W
Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b).
x-a
f(x)=
1 - cos (4x-4)
3(x-1)²
; a = 1
a. Use a graphing utility to graph f. Select the correct graph below..
A.
W
→
✓
Each graph is displayed in a [- 1,3] by [0,5] window.
B.
in
✓
○ C.
und
☑
Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
x-1
○ A. The limit appears to be approximately ☐ .
(Round to the nearest tenth as needed.)
B. The limit does not exist.
b. Evaluate f(x) for values of x near 1 to support your conjecture.
X
0.9
0.99
0.999
1.001
1.01
1.1
f(x)
○ D.
+
☑
(Round to six decimal places as needed.)
Does the table from the previous step support your conjecture?
A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…
x²-19x+90
Let f(x) =
.
Complete parts (a) through (c) below.
x-a
a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
x→a+
○ A.
a=
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There are no values of a for which the limit equals a finite number.
b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
x→a+
A.
(Type integers or simplified fractions)
C. There are no values of a that satisfy lim f(x) = ∞.
+
x-a
c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
x→a+
A. Either a
(Type integers or simplified fractions)
B.
Chapter 6 Solutions
Elementary Technical Mathematics
Ch. 6.1 - Solve each equation and check: x+2=8Ch. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Solve each equation and check: 23n=6Ch. 6.1 - Solve each equation and check: w712=3Ch. 6.1 - Prob. 6ECh. 6.1 - Solve each equation and check: x13=1.5Ch. 6.1 - Solve each equation and check: n+12=5Ch. 6.1 - Solve each equation and check: 3b=15.6Ch. 6.1 - Solve each equation and check: y17=25
Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Solve each equation and check: 2=x5Ch. 6.1 - Prob. 14ECh. 6.1 - Solve each equation and check: 17=3+wCh. 6.1 - Solve each equation and check: 49=32+wCh. 6.1 - Solve each equation and check: 14b=57Ch. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Solve each equation and check: x+5=5Ch. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Solve each equation and check: 5x125=0Ch. 6.1 - Solve each equation and check: x7=56Ch. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Solve each equation and check: x=2Ch. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Solve each equation and check: 103x=16Ch. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Solve each equation and check: x5+4=9Ch. 6.1 - Solve each equation and check: 2x=6Ch. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Solve each equation and check: 3x5=12Ch. 6.1 - Prob. 42ECh. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Solve each equation and check: 2x3=7Ch. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Solve each equation and check: 28=73rCh. 6.1 - Solve each equation and check: 5x=6Ch. 6.1 - Prob. 50ECh. 6.1 - Solve each equation and check: 54y13=17.8Ch. 6.1 - Prob. 52ECh. 6.1 - Solve each equation and check: 28w56=8Ch. 6.1 - Prob. 54ECh. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Solve each equation and check: 313y=41Ch. 6.1 - Prob. 58ECh. 6.1 - Solve each equation and check: 83=174xCh. 6.1 - Solve each equation and check: 58=5m+52Ch. 6.2 - Solve each equation and check: 4y+9=7y15Ch. 6.2 - Solve each equation and check: 2y45=yCh. 6.2 - Solve each equation and check: 5x+3=7x5Ch. 6.2 - Prob. 4ECh. 6.2 - Solve each equation and check: 2x+7=5x21Ch. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Solve each equation and check: 3x+17=6x37Ch. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Solve each equation and check: 5y+12=12y5Ch. 6.2 - Solve each equation and check: 3x2=5x+8Ch. 6.2 - Prob. 14ECh. 6.2 - Solve each equation and check: 4x+25=6x45Ch. 6.2 - Prob. 16ECh. 6.2 - Solve each equation and check: 5x+4=10x7Ch. 6.2 - Solve each equation and check: 3x2=5x20Ch. 6.2 - Solve each equation and check: 27+5x=9+3xCh. 6.2 - Solve each equation and check: 2y+8=5y1Ch. 6.2 - Solve each equation and check: 7x+18=11x36Ch. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Solve each equation and check: 4x+2=8x7Ch. 6.2 - Solve each equation and check: 6x1=9x9Ch. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Solve each equation and check: 3x+1=17xCh. 6.2 - Solve each equation and check: 174y=14yCh. 6.3 - Solve each equation and check: 2(x+3)6=10Ch. 6.3 - Solve each equation and check: 3x+5(x6)=32Ch. 6.3 - Prob. 3ECh. 6.3 - Solve each equation and check: 5m(2m7)=5Ch. 6.3 - Solve each equation and check: 16=3(x4)Ch. 6.3 - Prob. 6ECh. 6.3 - Solve each equation and check: 5a(3a+4)=8Ch. 6.3 - Prob. 8ECh. 6.3 - Solve each equation and check: 5a4(a3)=7Ch. 6.3 - Prob. 10ECh. 6.3 - Prob. 11ECh. 6.3 - Solve each equation and check: 278(2y)=13Ch. 6.3 - Solve each equation and check: 2a(5a7)=22Ch. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Solve each equation and check: 3x7+17(1x)=6Ch. 6.3 - Prob. 18ECh. 6.3 - Solve each equation and check: 6b=27+3bCh. 6.3 - Solve each equation and check: 2a+4=a3Ch. 6.3 - Solve each equation and check: 4(25x)=3x+2Ch. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - Solve each equation and check: 6x+2=2(17x)Ch. 6.3 - Solve each equation and check: 6(17x)=24xCh. 6.3 - Prob. 27ECh. 6.3 - Prob. 28ECh. 6.3 - Solve each equation and check: 3(x+4)+3x=6Ch. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - Solve each equation and check: 9m3(m5)=7m3Ch. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Solve each equation and check: 8(x5)=13xCh. 6.3 - Prob. 38ECh. 6.3 - Prob. 39ECh. 6.3 - Prob. 40ECh. 6.3 - Solve each equation and check:...Ch. 6.3 - Prob. 42ECh. 6.3 - Prob. 43ECh. 6.3 - Prob. 44ECh. 6.3 - Solve each equation and check: 4(y+2)=8(y4)+7Ch. 6.3 - Prob. 46ECh. 6.3 - Solve each equation and check:...Ch. 6.3 - Prob. 48ECh. 6.3 - Solve each equation and check: 12+8(2y+3)=(y+7)16Ch. 6.3 - Prob. 50ECh. 6.3 - Prob. 51ECh. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.3 - Solve each equation and check: 2(5y+1)+16=4+3(y7)Ch. 6.3 - Prob. 55ECh. 6.3 - Prob. 56ECh. 6.3 - Solve each equation and check:...Ch. 6.3 - Prob. 58ECh. 6.3 - Prob. 59ECh. 6.3 - Prob. 60ECh. 6.4 - Solve each equation and check: 2x3=326Ch. 6.4 - Solve each equation and check: 5x7=2014Ch. 6.4 - Prob. 3ECh. 6.4 - Solve each equation and check: 53x=1313Ch. 6.4 - Solve each equation and check: 212x=712Ch. 6.4 - Solve each equation and check: 12+x3=52Ch. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Solve each equation and check: 34x3=512Ch. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Solve each equation and check: 2x37=x2Ch. 6.4 - Solve each equation and check: y31=y6Ch. 6.4 - Prob. 14ECh. 6.4 - Solve each equation and check: 3x4720=25xCh. 6.4 - Solve each equation and check: 5x6+13(6+x)=37Ch. 6.4 - Solve each equation and check: x2+23(2x+3)=46Ch. 6.4 - Solve each equation and check: 16x19(2x3)=1Ch. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - Solve each equation and check: 3x24163x1212=3Ch. 6.4 - Prob. 22ECh. 6.4 - Solve each equation and check: 5x+6x814+10x+66=43Ch. 6.4 - Prob. 24ECh. 6.4 - Solve each equation and check: 4x6x+52=6x68Ch. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Solve each equation and check: 51x=7Ch. 6.4 - Solve each equation and check: 3x6=8Ch. 6.4 - Prob. 31ECh. 6.4 - Solve each equation and check: 17x=8Ch. 6.4 - Solve each equation and check: 3x8=7Ch. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prob. 36ECh. 6.4 - Solve each equation and check: 6x+5=14Ch. 6.4 - Prob. 38ECh. 6.4 - Solve each equation and check: 12x=143x13Ch. 6.4 - Prob. 40ECh. 6.4 - Prob. 41ECh. 6.4 - Solve each equation and check: 8x+14=5x+13Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Prob. 2ECh. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Prob. 4ECh. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Prob. 8ECh. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Prob. 14ECh. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Prob. 19ECh. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Prob. 22ECh. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Translate each phrase or sentence into algebraic...Ch. 6.5 - Prob. 25ECh. 6.6 - A built-in bookcase containing eight book shelves...Ch. 6.6 - Saw a board 8 ft 4 in. long into nine equal...Ch. 6.6 - Separate an order of 256 light fixtures so that...Ch. 6.6 - Distribute $1000 into three parts so that one part...Ch. 6.6 - Distribute $4950 among John, Maria, and Betsy so...Ch. 6.6 - Distribute $4950 among John, Maria, and Betsy so...Ch. 6.6 - A rectangle is twice as long as it is wide. Its...Ch. 6.6 - The length of a rectangle is 4 cm less than twice...Ch. 6.6 - One side of a rectangular yard is bounded by the...Ch. 6.6 - A given type of concrete contains an amount of...Ch. 6.6 - The perimeter of a triangle is 122 ft. The lengths...Ch. 6.6 - Cut a board 20 ft long into three pieces so that...Ch. 6.6 - Cut a 12-ft beam into two pieces so that one piece...Ch. 6.6 - The total cost of three automobile batteries is...Ch. 6.6 - The total cost of 20 boards is $166. One size...Ch. 6.6 - Amy and Kurt earned a total of $512 by working a...Ch. 6.6 - Joyce invests $7500 in two savings accounts. One...Ch. 6.6 - Chuck receives loans totaling $12,000 from two...Ch. 6.6 - Regular milk has 4% butterfat. How many litres of...Ch. 6.6 - How much pure alcohol must be added to 750 mL of a...Ch. 6.6 - Mix a solution that is 30% alcohol with a solution...Ch. 6.6 - Prob. 22ECh. 6.6 - A 12-quart cooling system is checked and found to...Ch. 6.6 - In testing an engine, various mixtures of gasoline...Ch. 6.6 - Assume you have sea water that weighs 64lb/ft3 and...Ch. 6.6 - Prob. 26ECh. 6.6 - Jeff invested $30,000 in a business whereas his...Ch. 6.6 - Prob. 28ECh. 6.6 - Cloth table coverings are to be cut for 8...Ch. 6.6 - How many quarts of water must be added to 3 gal of...Ch. 6.6 - Ground beef that is 90% lean costs 114 times the...Ch. 6.7 - Solve each formula for the given letter: E=IrforrCh. 6.7 - Solve each formula for the given letter: A=bhforbCh. 6.7 - Solve each formula for the given letter: F=maforaCh. 6.7 - Prob. 4ECh. 6.7 - Solve each formula for the given letter: C=dfordCh. 6.7 - Solve each formula for the given letter: V=IRforRCh. 6.7 - Solve each formula for the given letter: V=lwhforwCh. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Solve each formula for the given letter: A=2rhforhCh. 6.7 - Solve each formula for the given letter: C=2rforrCh. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Prob. 12ECh. 6.7 - Solve each formula for the given letter: I=QtfortCh. 6.7 - Prob. 14ECh. 6.7 - Prob. 15ECh. 6.7 - Solve each formula for the given letter: I=EZforZCh. 6.7 - Solve each formula for the given letter: I=VRforRCh. 6.7 - Prob. 18ECh. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Solve each formula for the given letter: R=2PforPCh. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Prob. 22ECh. 6.7 - Prob. 23ECh. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Prob. 26ECh. 6.7 - Prob. 27ECh. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Prob. 30ECh. 6.7 - Prob. 31ECh. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Prob. 34ECh. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Prob. 38ECh. 6.7 - Prob. 39ECh. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Solve each formula for the given letter:...Ch. 6.7 - Solve each formula for the given letter:...Ch. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - Prob. 2ECh. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - Prob. 4ECh. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - Prob. 6ECh. 6.8 - Prob. 7ECh. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - Prob. 10ECh. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - a. Solve for the indicated. b. Then substitute the...Ch. 6.8 - Prob. 20ECh. 6.8 - Prob. 21ECh. 6.8 - A flashlight bulb is connected to a 1.50-V source....Ch. 6.8 - Prob. 23ECh. 6.8 - The volume of a box is given by V=lwh. Find the...Ch. 6.8 - The volume of a cylinder is given by the formula...Ch. 6.8 - The pressure at the bottom of a lake is found by...Ch. 6.8 - The equivalent resistance R of two resistances...Ch. 6.8 - The R value of insulation is given by the formula...Ch. 6.8 - A steel railroad rail expands and contracts...Ch. 6.8 - The inductive reactance, XL, of a coil is given by...Ch. 6.9 - Use the formula 1R=1R1+1R2 for Exercise 1-6: Given...Ch. 6.9 - Use the formula 1R=1R1+1R2 for Exercise 1-6: Given...Ch. 6.9 - Use the formula 1R=1R1+1R2 for Exercise 1-6: Given...Ch. 6.9 - Prob. 4ECh. 6.9 - Prob. 5ECh. 6.9 - Prob. 6ECh. 6.9 - Prob. 7ECh. 6.9 - Prob. 8ECh. 6.9 - Use the formula 1f=1s0+1si for Exercises 7-10:...Ch. 6.9 - Use the formula 1f=1s0+1si for Exercises 7-10:...Ch. 6.9 - Prob. 11ECh. 6.9 - Prob. 12ECh. 6.9 - Use the formula 1R=1R1+1R2+1R3 for Exercise 11-16:...Ch. 6.9 - Prob. 14ECh. 6.9 - Prob. 15ECh. 6.9 - Prob. 16ECh. 6.9 - Prob. 17ECh. 6.9 - Use the formula 1C=1C1+1C2+1C3 for Exercise 1-22:...Ch. 6.9 - Prob. 19ECh. 6.9 - Prob. 20ECh. 6.9 - Prob. 21ECh. 6.9 - Prob. 22ECh. 6.9 - Prob. 23ECh. 6.9 - Prob. 24ECh. 6 - Solve each equation and check: 2x+4=7Ch. 6 - Prob. 2RCh. 6 - Prob. 3RCh. 6 - Prob. 4RCh. 6 - Prob. 5RCh. 6 - Prob. 6RCh. 6 - Solve each equation and check: 2x+9=5x15Ch. 6 - Prob. 8RCh. 6 - Prob. 9RCh. 6 - Solve each equation and check: 4x+1=4xCh. 6 - Solve each equation and check: 7(x5)=11Ch. 6 - Prob. 12RCh. 6 - Prob. 13RCh. 6 - Solve each equation and check: 6(x+7)5(x+8)=0Ch. 6 - Prob. 15RCh. 6 - Prob. 16RCh. 6 - Solve each equation and check: 2x3=169Ch. 6 - Prob. 18RCh. 6 - Solve each equation and check: 3x4x15=3+x2Ch. 6 - Prob. 20RCh. 6 - Prob. 21RCh. 6 - The length of rectangle is 6 more than twice its...Ch. 6 - Mix a solution that is 60% acid with a solution...Ch. 6 - Solve each formula for the given letter: F=WgforgCh. 6 - Solve each formula for the given letter: P=WAforACh. 6 - Solve each formula for the given letter:...Ch. 6 - Solve each formula for the given letter:...Ch. 6 - Solve each formula for the given letter:...Ch. 6 - Solve each formula for the given letter:...Ch. 6 - Solve each formula for the given letter:...Ch. 6 - Prob. 31RCh. 6 - Prob. 32RCh. 6 - Prob. 33RCh. 6 - Prob. 34RCh. 6 - Solve each equation: x8=6Ch. 6 - Solve each equation: 4x=60Ch. 6 - Prob. 3TCh. 6 - Prob. 4TCh. 6 - Prob. 5TCh. 6 - Solve each equation: 2(x+10)=3(52x)+5Ch. 6 - Solve each equation: 12(3x6)=3(x2)Ch. 6 - Solve each equation: 8x9=56Ch. 6 - Solve each equation: 3x52=x5x10Ch. 6 - Solve each equation: 8x+6=2Ch. 6 - Solve each equation: x225=2x534Ch. 6 - Distribute $2700 among Jose, Maria, and George so...Ch. 6 - How much pure antifreeze must be added to 20 L of...Ch. 6 - Solve P=2(l+2)forlCh. 6 - Solve CT=C1+C2+C3forC2.Ch. 6 - Solve V=lwhforw.Ch. 6 - Given P=I2R,P=480,andl=5.0,findR.Ch. 6 - Given A=h2(a+b),A=260,h=13,anda=15,findbCh. 6 - Given 1C=1C1+1C2,C=20.0FandC2=30.0F,findC1.Ch. 6 - Given 1R=1R1+1R2+1R3,R1=225,R2=475,andR3=925,findRCh. 6 - Prob. 1CRCh. 6 - Prob. 2CRCh. 6 - Write 3.015104 in decimal form.Ch. 6 - Prob. 4CRCh. 6 - Prob. 5CRCh. 6 - Prob. 6CRCh. 6 - Prob. 7CRCh. 6 - Prob. 8CRCh. 6 - Read the measurement shown on the vernier caliper...Ch. 6 - Prob. 10CRCh. 6 - Prob. 11CRCh. 6 - Prob. 12CRCh. 6 - Prob. 13CRCh. 6 - Prob. 14CRCh. 6 - Prob. 15CRCh. 6 - Prob. 16CRCh. 6 - Simplify: (4x3y)(5x+2y)Ch. 6 - Simplify: 215x2y345x3y5Ch. 6 - Prob. 19CRCh. 6 - Prob. 20CRCh. 6 - Prob. 21CRCh. 6 - Prob. 22CRCh. 6 - Prob. 23CRCh. 6 - Prob. 24CRCh. 6 - Prob. 25CRCh. 6 - Prob. 26CRCh. 6 - Prob. 27CRCh. 6 - Prob. 28CRCh. 6 - Prob. 29CRCh. 6 - The perimeter of a rectangle is 30 ft. The width...
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- Sketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the following conditions. f(2)=0 f(4) is undefined lim f(x)=1 X-6 lim f(x) = -∞ x-0+ lim f(x) = ∞ lim f(x) = ∞ x-4 _8arrow_forwardNo chatgpt pls will upvote Already got wrong chatgpt answerarrow_forwardNo chatgpt pls will upvote Already got wrong chatgpt answerarrow_forwardDetermine the following limit. lim 35w² +8w+4 w→∞ √49w+w³ 3 Select the correct choice below, and, if necessary, fill in the answer box to complete your choice. ○ A. lim W→∞ 35w² +8w+4 49w+w3 (Simplify your answer.) B. The limit does not exist and is neither ∞ nor - ∞.arrow_forwardCalculate the limit lim X-a x-a 5 using the following factorization formula where n is a positive integer and x-➡a a is a real number. x-a = (x-a) (x1+x-2a+x lim x-a X - a x-a 5 = n- + xa an-2 + an−1)arrow_forwardThe function s(t) represents the position of an object at time t moving along a line. Suppose s(1) = 116 and s(5)=228. Find the average velocity of the object over the interval of time [1,5]. The average velocity over the interval [1,5] is Vav = (Simplify your answer.)arrow_forwardFor the position function s(t) = - 16t² + 105t, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 1. Time Interval Average Velocity [1,2] Complete the following table. Time Interval Average Velocity [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] [1,2] [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] ப (Type exact answers. Type integers or decimals.) The value of the instantaneous velocity at t = 1 is (Round to the nearest integer as needed.)arrow_forwardFind the following limit or state that it does not exist. Assume b is a fixed real number. (x-b) 40 - 3x + 3b lim x-b x-b ... Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (x-b) 40 -3x+3b A. lim x-b x-b B. The limit does not exist. (Type an exact answer.)arrow_forwardx4 -289 Consider the function f(x) = 2 X-17 Complete parts a and b below. a. Analyze lim f(x) and lim f(x), and then identify the horizontal asymptotes. x+x X--∞ lim 4 X-289 2 X∞ X-17 X - 289 lim = 2 ... X∞ X - 17 Identify the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has a horizontal asymptote at y = B. The function has two horizontal asymptotes. The top asymptote is y = and the bottom asymptote is y = ☐ . C. The function has no horizontal asymptotes. b. Find the vertical asymptotes. For each vertical asymptote x = a, evaluate lim f(x) and lim f(x). Select the correct choice and, if necessary, fill in the answer boxes to complete your choice. earrow_forwardExplain why lim x²-2x-35 X-7 X-7 lim (x+5), and then evaluate lim X-7 x² -2x-35 x-7 x-7 Choose the correct answer below. A. x²-2x-35 The limits lim X-7 X-7 and lim (x+5) equal the same number when evaluated using X-7 direct substitution. B. Since each limit approaches 7, it follows that the limits are equal. C. The numerator of the expression X-2x-35 X-7 simplifies to x + 5 for all x, so the limits are equal. D. Since x²-2x-35 X-7 = x + 5 whenever x 7, it follows that the two expressions evaluate to the same number as x approaches 7. Now evaluate the limit. x²-2x-35 lim X-7 X-7 = (Simplify your answer.)arrow_forwardA function f is even if f(x) = f(x) for all x in the domain of f. If f is even, with lim f(x) = 4 and x-6+ lim f(x)=-3, find the following limits. X-6 a. lim f(x) b. +9-←x lim f(x) X-6 a. lim f(x)= +9-←x (Simplify your answer.) b. lim f(x)= X→-6 (Simplify your answer.) ...arrow_forwardEvaluate the following limit. lim X-X (10+19) Select the correct answer below and, if necessary, fill in the answer box within your choice. 10 A. lim 10+ = 2 ☐ (Type an integer or a simplified fraction.) X-∞ B. The limit does not exist.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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