Questions

a f x 1 M 2 1 0 1 1 Find g 2 g 2 and g 2 2 5 6 7 8 The function f is continuous on the interval 2 7 and consists of three line segments and a semi circle as shown in the figure above The function g is defined by g x d Let h x f 5x 9 Find h 3 2 X J f t dt 2 b Find the x coordinate of the critical points on g x on the interval 2 7 Classify each critical point found in part b as a relative minimum relative maximum or neither for g Justify your answers c Find the interval s where g is increasing and concave down Justify your answer

Find the domain of the function 15 2 3 on Q

Problem 7 Let f x 1 0 8 x 1 2 Suppose that we approximate f x by the 4th degree Taylor polynomial T4 x centered at a 1 Taylor s inequaltiy gives an estimate for the error involved in this approximation Find the smallest possible value of the constant M referred to in Taylor s Inequality Problem 7 Your answer cannot contain any decimal 0 00122 points 0 00122 Enter your answer symbolically as in these examples

Choose all of the following that are ways we can interpret or apply the derivativ the slope of the tangent line the average rate of change the instantaneous rate of change O the slope of the secant line

Work required Find the derivative of the function O O 0 1 2 2 5z 1 O2 52 1 55 8 2z 1 6 52 1 4z2 SU 52 1 2 3

No work required Identify the derivative of f x sec 2x O sec 41 O 4r tan 22 47 sec 27 tan 27 O COS 4x O sec 42 tan 47

Work required Find the slope of the curve at the given point Hint use implicit differentiation y x y 2r 2 1

y 1 47 e 0 22t cos 4 9t ere y is the displacement in feet and t is the time in seconds Use a graphing utility to graph the displacement function for 0 t 10 Find t e beyond which the distance between the weight and equilibrium does not exceed 0 85 ft Round your answer to 2 decimal places S

Which is the standard linear approximation of a function at x a L z f a z a OL z f a f a x a OL T f a f a z a O L T f a ra O None of the above

No work required Identify the derivative of f x 2e O 6e O 2e3 00

Work required Given the position s f t of a body with s in meters and t in seconds find the body s acceleration each time the velocity is zero s t 6t 9t Enter the answer here acceleration If you have more than one value separate the answers with commas Enter fractions as a ratio if needed e g 1 4 and omit units

Work required Find the derivative of the function 0 72 7 2 1 1 0 1 0 72 7 1 1 072 7 0 72 7 0 7z 7 1 y z 7x 1

No work required Identify the derivative of f x 4 2x x O 2 32 2 O 2 31 2 O 2 3x4 O4z 2 37

O tan 12 O 12 sec 12 O 12 sec 12r tan 122 12 1 144x2 O Identify the derivative of f x tan 12x O 1 144z sec 122

Work required Enter answers below omitting units and keep answers exact i e do not estimate but include in your answer appropriate You may write pi if you like A spherical balloon is inflated with helium at a rate of 100 ft min Note V and S 4TT2 A How fast is the balloon s radius increasing at the instant the radius is 5 ft B How fast is the surface area increasing

O2 In sec 0 tan 0 Work required Find the derivative of the function O 2 tan 0 O O 2 sec 0 2 SMC Lan f 0 In sec 0

Match each compound statement to its symbolic form g r p rq p p q r q The topic of logic is interesting r I do not miss class rp q p q Ar r p g r pv q p q r r q V p p q T a I do not miss class if and only if I like math and the topic of logic is interesting b If I miss class then the topic of logic is not interesting or I like math c I like math and if the topic of logic is interesting then I do not miss class d I do not miss class if and only if the topic of logic is interesting and I like math e I like math if and only if the topic of logic is interesting and I do not miss class f If I miss class then it isn t true that I like math and the topic of logic is interesting g If it isn t true that I like math and I find the topic of logic interesting then I miss class h If I like math and the topic of logic is interesting then I do not miss class i If I miss class then I don t like math or the topic of logic is not interesting j If the topic of logic is interesting and I do not miss class then I like math

Determine the truth value of each compound statement when p is false q is true and ris false p r pv g P q r p q r P q r P q r Question Help Video Message instructor F T v

Find the missing factor in the following expressio 7x 2 7 x 2 7X 2 7x 2 7 2 7x 2

Fill in the blanks in the following truth table Pq P p q p q V p TT TF V v v FT v FF v v

simple statements p The water is warm q The sun is shining r We go swimming Match each compound statement to its symbolic form If the water is not warm then the sun is shining or we go swimming The sun is shining if and only if the water is warm and we go swimming If the sun is shining then the water is warm or we go swimming If the sun is shining and we go swimming then the water is warm If we don t go swimming then the sun is shining and the water is warm The water is not warm and the sun is shining or we go swimming If the sun is shining then we go swimming and the water is warm The water is warm or the sun is shining and we don t go swimming If the sun is shining then the water is warm if and only if we go swimming The water is warm and the sun is shining or we go swimming a q p Vr b pVg r c q p Ar d p qVr e q r p f r q P g q r p h p qVr i p g Vr

Let p and q represent the following statements p You study hard q You graduate with honors Write the following statement in symbolic form You don t study hard or you don t graduate with honors To enter your response select the appropriate statement in each of the dropdown boxes and select the appropriate operation in the middle If only one statement is used select none for the operation in the middle and the statement in the second dropdown box Be sure to enter the statements in the same order as in the given sentence O AO V Onone Select an answer

For the simple statements p It is a frog q It has feathers Write each compound statement in symbolic form V It is a frog if and only if it has feathers If it has feathers then it is a frog If it is not a frog then it has feathers

2 Count the number of breaths taken in 1 minute Note the depth of breathing at one of three levels Record the data in TABLE 21 8 Table 21 8 Factors Affecting Rate and Depth of Breathing Test Factor Normal breathing Breath holding Rebreathing air Breathing Rate breaths minute Breathing Depth

Consider the set of whole numbers from 1 to 10 inclusive List the numbers that meet the condition less than three and odd

For each expression below write an equivalent expression that involves x only Assume x is positive 69 cos cos x 70 sin sin x 71 cos sin x

Use a calculator to evaluate each expression to the nearest tenth of a degree 39 sin 0 1702 40 sin 0 1702 41 cos 0 8425

2 21 52

Evaluate without using a calculator 3 n 1 4 53 cos tan 56 tan cos 54 csc tan 1 55 tan sin 1 58 sin cos 1 5 57 sec cos V 5

13 Match the correct answer Given WXYZ is a parallelogram XZL WY Prove WXYZ is a rhombus Statements 1 WXYZ is a parallelogram 2 XZLWY 3 2WPX and 4 LWPX and Reasons 1 Given 2 Given XPY are 90 s 3 Def of lines XPY are rt Zb 4 e 5 AWPX and AYPX are rt As 5 Def of rt As XP XP 0 e 7 XZ bisects WY 7 Diags of a bisect each other 8 Def of bisector WP PY 9 9 LL 10 WXXY 10 CPCTC 11 11 with one pair of consecutive sides thom AWPXAYPX b AWPX AYPZ c Reflexove Property of d Transitive Property of

Find the missing factor in the following expression 36 h 36 36 h 36

Solve the following equation for x Let X 3x 32x 90 3x 729 0 X

Write each expression in the form 2kx or 3kx for a suitable constant k 2x 17 3 27 a 2x a 1 b 3x c 16 x 2

Write each expression in the form 2kx or 3kx for a suitable constant k a 8x b 2 c

Write each expression in the form 2kx or 3kx for a suitable constant k a a 24x h 24x2 3x 2 3x 2

Write each expression in the form 2kx or 3kx for a suitable constant 3 3x 1 3 3 2x a 37x 33x 37x a 11 b 4 X 8 x 3 c

Solve the following equation for x 53x 56 x

Solve the following equation for x 5X 3 5 9 2 5 X

Find a number c such that the function f x 3 3x can be written in the form f x cx

olve the following equation for x 1 7 2x 1 1 7 5

Solve the following equation for x 10 6 x 100 x

The domain of a function is the set of all first coordinates the set of all values that x can assume The range is the set of all second coordinates all the values that y can assume 15 What is the domain of the function y sin x

Simplify 19 sin 1 3 2 23 tan 11 20 cos 2 24 tan 0 21 cos 1 22 cos 0 1 2 25 arccos 26 arccos 1

Simplify 19 sin 1 V3 2 23 tan 1

alliance and enmity all played a part in shaping different Indian nations geographic dominion Yet no matter the political economy all of them governed and defended bounded sovereign domains Let us look briefly at those three case studies in Texas and the southern plains in order to get the conversation about Native borders going It is often assumed that hunter gatherers may be better understood for what they lacked as opposed to what they had but they maintained clearly delineated ethnic domains defined by kinship and marriage For hunter gatherers such as Coahuilteco and Karankawa speakers territories were maintained often shared spaces of control within which certain groups exclusive rights to collective ranges and resources The allegiances among the groups meant that they joined together to hunt and to defend the lands they held in common The boundaries of their territory were well estab lished known to all and marked by natural sites such as rivers or bays and manmade phenomena such as watering holes petroglyphs pictographs or painted trees Trespass was a legal concept and once Europeans arrived in the region they were subject to that charge Sedentary agriculturalists such as Caddos exercised control over a more expansive bordered domain made up of rings of settlement Hunting ter ritories manned and defended by small family groups in hunting lodges made up the outermost ring Moving inward the next ring was a space made up of farming homesteads surrounded by cultivated fields and small hamlets each represented by a subchief At the core one found the cer emonial complex and primary township of the head political and religious Caddo leadership To secure their domain Caddos had border control as well as passport and surveillance systems and within their territory were internal boundaries between member nations For mobile groups such as Comanches and Apaches raiding served geo political as well as economic purpose in aiding territorial expansion Both groups evinced clear growth strategies by extending control over greater and greater subsistence zones Their boundaries might move regularly but that did not diminish the security of their borders indeed mobility was the key to border defense and resource management within extensive territories Apaches and Comanches too marked their borders with land marks cairns and trees made to grow in particular forms or directions Thus when Europeans arrived all set to colonize the region they found their border making aspirations ran smack up against the border defense and horder expansion of Indian nations Spaniards and Frenchmen found nnires they had to seek

2015 University of North 300 300 Mundey PACIFIC OCEAN Mexica Empire Barra de Navidad NORTH AMERICA Quivira NE COMM Hudson Bay Gulf of Mexico Sedacone San Miguel de Gualdape 1526 Fort Caroline 1564 45 St Augustine 1565 Cuba Bahamas 10 Jamaica Santiago de Cabe ATLANTIC OCEAN Caribbean Sea 8 25 6 3 Puerto Rico FIGURE 1 2 The Spanish and French Invade North America 1519 1565 From Michael Schaller et al vol 1 of American Horizons U S History in a Global Context New York Oxford University Press 2012 29 By permission of Oxford University Press U S A At this point colored lines begin to appear marking the different routes of intrepid Europeans with lvar N ez Cabeza de Vaca Hernando de Soto Jacques Cartier Samuel Champlain Giovanni da Verrazzano and later John Smith competing to cover greater distances and claim more territory for their rulers Political borders first make an appearance in textbook maps of America only with the establishment of the British colonies New France New Netherlands and New Spain all of them new creations that rewrite historical spaces as European and in so doing deny the past of America s indigenous populations According to this cartographic vision there are no old worlds in the Americas Only then does America have towns for the first time Quebec Montreal Boston Jamestown New Orleans Santa Fe The most ubiquitous map design for this period of American history divides the continent into Spanish English and French territories draw ing borders for European claims far beyond the geographical reach of lors did

Native acceptance and permission to build settlements trading posts and missions within recognized Indian domains Indian homelands brushed up against one another their edges and peripheries creating zones of shared and contested indigenous dominion The lines drawn between Indian polities more often than not took precedence over newer bound aries drawn between themselves and Europeans even long after Spanish French and English arrival As it turns out my scholarly concern with Indians borders as out lined above grew out of frustrations in the classroom teaching American history frustration with two things particularly One is the conceptual notion that as soon as Europeans put their first big toes on the American coast all the Americas became a borderland up for grabs to the first European taker a notion that denies Indian sovereignty control of the land and basic home field advantage The second thing that set me off was the way in which our textbooks encourage this cockeyed vision of America with their maps Taking these two issues in turn the concept of borderlands sometimes appears to be used alongside or in place of frontiers but either when way we map it out on the ground it remains essentially a European defined space In American history borderlands frontiers hinterlands and back country customarily refer to the edges and peripheries of European and Euro American occupation and the limits of their invasion expansion conquest and settlement where Europeans and Euro Americans confront Indians or rival European powers Like frontiers borderlands appear just beyond the reach or sphere of centralized power associated with imperial European governance Like frontiers borderlands are zones in front of the hinterlands of Euro American settlement or in between rival European settlements think of the Spanish borderlands that are caught between the core of Latin America and the expansionary Anglo American world Either way they are supposed to be untamed unbounded wilder nesses waiting to be taken in hand by civilized Euro Americans Frontiers and borderlands are far from the imperial cores of France Spain Britain and later the United States and by definition are absent of a monopoly of power or violence So on the one hand these are spaces into which Euro Americans go without the force of the state or military near at hand Such conditions by implication are what make it possible for Indians to stand on equal ground to negotiate and to struggle for advantage But critically Indians ability to stand their ground and to thing to do with capabilities of their own

STRIKES WALK OUTS DISORDER RIOTS BOLSHEVISM MURDERS CHAOS OTEP BY STEP Gross is the New York Svealog Telegram What is the cartoonist s point of view in this 1919 politcal cartoon A Industrial production will expand and create more jobs B The actions of labor unions threaten the American way of life Immigrants will easily assimilate into American society Civil liberties will be restricted and ordinary American citizens will be hurt

the feedback in case you need to make any corrections Please make sure to include your work handwritten is preferable Graph the system of linear inequalities BY HAND Show the solution region Pay close attention to dashed solid lines and shading above below when graphing each inequality y 4x 2 x21 1 y S 10 8 6 4 2 y x 4 x 2y 6 10 1980 2 2 526 2 10 6 1226 4 2 2 4 6 8 10 Algebraically 2 5 54 2 4 521 4 545 4 false 6 8 10 2 y x This is true but since 2 5 does not satisfy it is Ihot a selution to the 10 8 6 4 10 2 57 8 o 6 5 4 2 3 Determine if 2 5 and 4 2 are solutions to the system of inequalities both algebraically and graphically Show your work algebraically Graphically draw and shade both inequalities Then plot each ordered pair to confirm the answers you found algebraically 15 2 4 6 8 10 2 4 Graphically Algebraically 4 2 4 2 226 4 4 6 836 This is true so 4 2 satisfies both inequalites 10 86 and is a solution to the systern 6 8 10 10 4 2 8 6 44 2 2 4 6000 4 6 8 10 2 4 6 8 10

From the 2013 IPE AB5 a Find g 6 and g 3 6 4 5 4 M 6 Graph of f 12 The graph of the continuous function f consisting of three line segments and a semicircle is shown above Let g be the function given by g x L f t dt b Find g 0 4 3 2 c Find all values of x on the open interval 6 x 3 for which the graph of g has a horizontal tangent Determine whether g has a local maximum a local minimum or neither at each of these values Justify your answers d Find all values of x on the open interval 6 x 3 for which the graph of g has a point of inflection Explain your reasoning