Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 14: Q. 12 (page 883)

In Problems 7– 42, find each limit algebraically

limx→4(-3x)

Short Answer

Expert verified

The value of the limitlimx→4(-3x)=-12

Step by step solution

01

Step 1. Given Information

The given limit and the function islimx→4(-3x)

We need to find the given limit.

02

Step 2. Expanding the limit 

We know,

limx→cf(x)·g(x)=limx→cf(x)limx→cg(x)

Therefore,

role="math" localid="1646939599725" limx→4(-3x)=limx→4(-3)limx→4x

03

Step 3. Applying limits

The obtained expression is

limx→4(-3x)=limx→4(-3)limx→4x

=[-3][4]=-12

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Problems 7– 42, find each limit algebraically.

limx→01-2x{"x":[[93,93,93,93,93,93,93,93,93,93,93,93,93,93,93],[115,115,115,115,115,115,115,115,115,115,115],[112],[112,112],[132,132,133,134,135,135,135,135,135,135,135,135,135,135,135,135,135,135,135,136,136,136,136,138,138,139,139,139,139,139,139,141,142,143,145,146,148,150,151,152,153,155,155,155,155,155,155,155,155,155,155,155,155,154,154,154,154,154,154,154,154,154,155,156,157,158,159,159,160,162,163,165,167,168,170,171,171,172,173,174,175,175,175,175,175,175,175,176,176],[90,91,91,95,98,100,103,104,106,107,107,107,107,107,106,105,104,104,104,104,104,104,104,104,104,104,104,104,104,104,104,104,104,105,106,106,107,108,110,111,113,115,115,117,118,119,118,116,113,111,109,106,105,103,103,102,101,101,101,101,102,104,105,107,109,111,111,113,114,115,115,116,118,119,119,120,121,122,123,123],[133,134,138,142,144,146,148,150,151,151,152,153,154,155,155,155,156,158,159,159,159,158,157,156,155,154,153,151,148,147,145,143,142,141,140,141,142,143,143,144,145,146,149,151,153,155,157,159,160,160,161,163,163,163,163,163,162,161,160,159,158,157,156,155,155,154,153],[182,182,182,182,182,182,182,182,182,182,182,182,182,182,182,182,182,182,182],[183,183,181,180,180,180,180,180,180,180,180,180,180,180,180,181,183,184,186,189,192,196,199,201,203,205,206,207,209,210,210,210,210,210,209,208,206,204,203,201,199,198,196,195,193,191,189,188,187,186,185,183,183],[212,213,215,219,223,225,228,230,231,233,234,234,235,235,235,235,234,231,231,229,228,227,227,227,227,227,227,227,227,227,227,227,227,227,229,231,237,250,261,273,287,295,302,313,320,327,337,340,343,347,348,351,353,355,356,357],[258,258,258,259,259,259,259,259,259,259,259,259,259,259,260],[298,304,310,316,319,321,325,327,328,329,330,331,331,331,332],[336,339,343,345,347,351,355,362,367,368,371,372,372,372,372,371,368,366,364,360,358,355,354,352,351,351,350,349,348,348,348,349,350,351,354,356,359,362,365,367,370,373,375,377,379,379,380,382,383],[383,384,386,388,390,391,393,395,395,396,396,396,396,396,396,396,396,396,396,396,396,396,396,396,395,394,393,392,391,391,391,391,391,391,392,393,394,395,397,399,400,402,403,404,405,406,405,404,403,403,402,401,399,397,396,395,395,394,393,392,392,392,392,392,392,393,395,396,397,398,399,402,403,403,404,405,406,407,407,408,409,410,411,411,412,413,414,415,415,416,417],[340,342,344,347,352,358,360,364,367,370,371,373,375,375,376,377,378,379,379,380,381,382,383,384,385,386,387,388,389,389,391,392,394,395,398,399,401,403,404,407,407,409,411,411,412,413,414]],"y":[[57.399993896484375,58.399993896484375,63.399993896484375,66.39999389648438,69.39999389648438,73.39999389648438,77.39999389648438,81.39999389648438,84.39999389648438,87.39999389648438,90.39999389648438,92.39999389648438,94.39999389648438,96.39999389648438,97.39999389648438],[81.39999389648438,83.39999389648438,85.39999389648438,90.39999389648438,93.39999389648438,97.39999389648438,99.39999389648438,101.39999389648438,104.39999389648438,105.39999389648438,106.39999389648438],[59.399993896484375],[59.399993896484375,59.399993896484375],[80.39999389648438,82.39999389648438,87.39999389648438,92.39999389648438,100.39999389648438,105.39999389648438,107.39999389648438,110.39999389648438,113.39999389648438,115.39999389648438,117.39999389648438,117.39999389648438,118.39999389648438,117.39999389648438,117.39999389648438,116.39999389648438,115.39999389648438,111.39999389648438,108.39999389648438,105.39999389648438,102.39999389648438,101.39999389648438,99.39999389648438,95.39999389648438,93.39999389648438,91.39999389648438,89.39999389648438,88.39999389648438,86.39999389648438,85.39999389648438,85.39999389648438,84.39999389648438,84.39999389648438,84.39999389648438,84.39999389648438,85.39999389648438,87.39999389648438,88.39999389648438,89.39999389648438,92.39999389648438,93.39999389648438,96.39999389648438,101.39999389648438,103.39999389648438,105.39999389648438,108.39999389648438,109.39999389648438,110.39999389648438,111.39999389648438,112.39999389648438,111.39999389648438,110.39999389648438,109.39999389648438,105.39999389648438,100.39999389648438,96.39999389648438,93.39999389648438,90.39999389648438,89.39999389648438,87.39999389648438,86.39999389648438,85.39999389648438,85.39999389648438,84.39999389648438,83.39999389648438,83.39999389648438,83.39999389648438,83.39999389648438,83.39999389648438,83.39999389648438,83.39999389648438,84.39999389648438,84.39999389648438,85.39999389648438,86.39999389648438,87.39999389648438,89.39999389648438,91.39999389648438,92.39999389648438,95.39999389648438,97.39999389648438,100.39999389648438,103.39999389648438,105.39999389648438,105.39999389648438,108.39999389648438,109.39999389648438,109.39999389648438,110.39999389648438],[136.39999389648438,136.39999389648438,136.39999389648438,138.39999389648438,140.39999389648438,143.39999389648438,146.39999389648438,149.39999389648438,150.39999389648438,153.39999389648438,156.39999389648438,159.39999389648438,161.39999389648438,162.39999389648438,164.39999389648438,166.39999389648438,167.39999389648438,168.39999389648438,169.39999389648438,168.39999389648438,167.39999389648438,166.39999389648438,165.39999389648438,165.39999389648438,164.39999389648438,163.39999389648438,161.39999389648438,159.39999389648438,156.39999389648438,154.39999389648438,152.39999389648438,149.39999389648438,146.39999389648438,145.39999389648438,142.39999389648438,141.39999389648438,140.39999389648438,137.39999389648438,137.39999389648438,135.39999389648438,134.39999389648438,133.39999389648438,133.39999389648438,132.39999389648438,131.39999389648438,131.39999389648438,132.39999389648438,133.39999389648438,136.39999389648438,136.39999389648438,138.39999389648438,141.39999389648438,142.39999389648438,144.39999389648438,145.39999389648438,145.39999389648438,146.39999389648438,147.39999389648438,148.39999389648438,149.39999389648438,149.39999389648438,151.39999389648438,153.39999389648438,154.39999389648438,156.39999389648438,157.39999389648438,157.39999389648438,158.39999389648438,158.39999389648438,158.39999389648438,158.39999389648438,158.39999389648438,158.39999389648438,159.39999389648438,159.39999389648438,159.39999389648438,159.39999389648438,159.39999389648438,159.39999389648438,160.39999389648438],[145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,144.39999389648438,144.39999389648438,144.39999389648438,143.39999389648438,142.39999389648438,141.39999389648438,141.39999389648438,141.39999389648438,141.39999389648438,141.39999389648438,141.39999389648438,141.39999389648438,140.39999389648438,138.39999389648438,138.39999389648438,137.39999389648438,136.39999389648438,136.39999389648438,135.39999389648438,135.39999389648438,135.39999389648438,135.39999389648438,135.39999389648438,136.39999389648438,137.39999389648438,137.39999389648438,137.39999389648438,140.39999389648438,141.39999389648438,143.39999389648438,145.39999389648438,145.39999389648438,145.39999389648438,146.39999389648438,147.39999389648438,148.39999389648438,149.39999389648438,149.39999389648438,150.39999389648438,151.39999389648438,152.39999389648438,153.39999389648438,153.39999389648438,154.39999389648438,155.39999389648438,157.39999389648438,157.39999389648438,158.39999389648438,159.39999389648438,160.39999389648438,160.39999389648438,160.39999389648438],[126.39999389648438,127.39999389648438,128.39999389648438,132.39999389648438,134.39999389648438,137.39999389648438,139.39999389648438,142.39999389648438,143.39999389648438,145.39999389648438,147.39999389648438,148.39999389648438,150.39999389648438,152.39999389648438,153.39999389648438,153.39999389648438,154.39999389648438,155.39999389648438,156.39999389648438],[129.39999389648438,135.39999389648438,140.39999389648438,143.39999389648438,145.39999389648438,149.39999389648438,150.39999389648438,153.39999389648438,155.39999389648438,156.39999389648438,157.39999389648438,158.39999389648438,159.39999389648438,160.39999389648438,161.39999389648438,161.39999389648438,161.39999389648438,161.39999389648438,161.39999389648438,161.39999389648438,161.39999389648438,160.39999389648438,159.39999389648438,158.39999389648438,157.39999389648438,157.39999389648438,156.39999389648438,155.39999389648438,153.39999389648438,152.39999389648438,151.39999389648438,150.39999389648438,149.39999389648438,147.39999389648438,145.39999389648438,143.39999389648438,140.39999389648438,138.39999389648438,137.39999389648438,134.39999389648438,134.39999389648438,133.39999389648438,132.39999389648438,131.39999389648438,131.39999389648438,131.39999389648438,131.39999389648438,131.39999389648438,131.39999389648438,131.39999389648438,131.39999389648438,131.39999389648438,131.39999389648438],[104.39999389648438,104.39999389648438,105.39999389648438,111.39999389648438,113.39999389648438,115.39999389648438,118.39999389648438,120.39999389648438,121.39999389648438,122.39999389648438,123.39999389648438,124.39999389648438,124.39999389648438,123.39999389648438,122.39999389648438,120.39999389648438,102.39999389648438,87.39999389648438,77.39999389648438,66.39999389648438,63.399993896484375,61.399993896484375,58.399993896484375,55.399993896484375,54.399993896484375,52.399993896484375,50.399993896484375,49.399993896484375,47.399993896484375,45.399993896484375,44.399993896484375,43.399993896484375,42.399993896484375,42.399993896484375,42.399993896484375,42.399993896484375,42.399993896484375,42.399993896484375,42.399993896484375,42.399993896484375,42.399993896484375,42.399993896484375,42.399993896484375,42.399993896484375,41.399993896484375,41.399993896484375,40.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375],[61.399993896484375,65.39999389648438,73.39999389648438,78.39999389648438,82.39999389648438,86.39999389648438,89.39999389648438,90.39999389648438,93.39999389648438,94.39999389648438,95.39999389648438,96.39999389648438,97.39999389648438,97.39999389648438,97.39999389648438],[83.39999389648438,81.39999389648438,79.39999389648438,78.39999389648438,77.39999389648438,77.39999389648438,77.39999389648438,77.39999389648438,77.39999389648438,77.39999389648438,77.39999389648438,77.39999389648438,77.39999389648438,76.39999389648438,76.39999389648438],[48.399993896484375,48.399993896484375,49.399993896484375,49.399993896484375,50.399993896484375,53.399993896484375,57.399993896484375,68.39999389648438,74.39999389648438,79.39999389648438,84.39999389648438,85.39999389648438,86.39999389648438,89.39999389648438,89.39999389648438,91.39999389648438,93.39999389648438,93.39999389648438,94.39999389648438,95.39999389648438,95.39999389648438,95.39999389648438,95.39999389648438,95.39999389648438,95.39999389648438,94.39999389648438,94.39999389648438,93.39999389648438,93.39999389648438,93.39999389648438,92.39999389648438,91.39999389648438,90.39999389648438,89.39999389648438,89.39999389648438,88.39999389648438,88.39999389648438,88.39999389648438,88.39999389648438,88.39999389648438,89.39999389648438,89.39999389648438,90.39999389648438,91.39999389648438,91.39999389648438,91.39999389648438,91.39999389648438,91.39999389648438,91.39999389648438],[65.39999389648438,65.39999389648438,66.39999389648438,69.39999389648438,69.39999389648438,73.39999389648438,76.39999389648438,78.39999389648438,80.39999389648438,83.39999389648438,85.39999389648438,89.39999389648438,93.39999389648438,96.39999389648438,99.39999389648438,101.39999389648438,102.39999389648438,104.39999389648438,105.39999389648438,104.39999389648438,103.39999389648438,102.39999389648438,101.39999389648438,100.39999389648438,94.39999389648438,92.39999389648438,87.39999389648438,84.39999389648438,81.39999389648438,80.39999389648438,78.39999389648438,76.39999389648438,73.39999389648438,73.39999389648438,71.39999389648438,69.39999389648438,68.39999389648438,67.39999389648438,65.39999389648438,64.39999389648438,62.399993896484375,61.399993896484375,61.399993896484375,60.399993896484375,59.399993896484375,59.399993896484375,59.399993896484375,60.399993896484375,61.399993896484375,61.399993896484375,62.399993896484375,63.399993896484375,64.39999389648438,65.39999389648438,66.39999389648438,68.39999389648438,69.39999389648438,70.39999389648438,72.39999389648438,72.39999389648438,73.39999389648438,74.39999389648438,75.39999389648438,76.39999389648438,77.39999389648438,78.39999389648438,80.39999389648438,81.39999389648438,83.39999389648438,84.39999389648438,85.39999389648438,85.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438,86.39999389648438],[39.399993896484375,39.399993896484375,39.399993896484375,39.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,38.399993896484375,37.399993896484375,37.399993896484375,37.399993896484375,37.399993896484375,37.399993896484375,37.399993896484375,37.399993896484375,37.399993896484375,37.399993896484375,36.399993896484375,36.399993896484375,35.399993896484375,35.399993896484375,35.399993896484375,35.399993896484375,34.399993896484375,33.399993896484375,33.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375,32.399993896484375]],"t":[[0,222,239,256,272,289,306,322,339,356,372,389,405,422,439],[1789,1994,2005,2023,2038,2055,2072,2088,2105,2122,2138],[3430],[3555,3558],[4610,4821,4838,4854,4871,4888,4904,4921,4938,4954,4971,4988,5004,5096,5111,5125,5139,5155,5171,5188,5204,5221,5238,5254,5271,5288,5304,5321,5338,5354,5371,5388,5416,5437,5454,5471,5487,5504,5521,5538,5554,5571,5587,5604,5621,5637,5654,5671,5687,5704,5778,5788,5804,5821,5837,5854,5871,5888,5904,5921,5938,5954,5971,5987,6004,6022,6037,6054,6071,6087,6104,6121,6137,6154,6171,6187,6204,6221,6237,6254,6271,6287,6304,6321,6337,6354,6371,6387,6404],[7792,8033,8041,8054,8070,8087,8104,8120,8137,8154,8170,8187,8205,8221,8237,8254,8271,8287,8304,8394,8409,8422,8437,8459,8470,8487,8504,8520,8537,8554,8570,8587,8603,8620,8637,8654,8670,8687,8704,8720,8737,8753,8770,8787,8803,8820,8920,8950,8971,8988,9004,9022,9038,9054,9070,9087,9104,9120,9154,9170,9187,9203,9220,9237,9253,9270,9287,9303,9320,9337,9353,9381,9420,9496,9510,9524,9546,9560,9574,9653],[11096,11354,11370,11386,11403,11419,11436,11453,11470,11486,11503,11529,11570,11620,11636,11653,11670,11686,11736,11765,11819,11849,11864,11878,11899,11920,11936,11953,11969,11986,12003,12020,12036,12053,12069,12147,12161,12175,12196,12209,12219,12236,12253,12269,12286,12303,12319,12336,12353,12369,12386,12403,12437,12453,12503,12519,12536,12553,12569,12586,12602,12619,12636,12652,12669,12686,12707],[13832,14060,14069,14085,14102,14119,14136,14152,14169,14185,14202,14219,14236,14252,14269,14285,14302,14319,14336],[18538,18752,18769,18784,18802,18819,18834,18852,18869,18884,18902,18918,18935,18952,18968,19001,19019,19035,19052,19069,19084,19103,19118,19135,19152,19168,19185,19202,19218,19235,19252,19267,19284,19302,19317,19335,19351,19368,19385,19401,19418,19435,19451,19468,19485,19501,19517,19535,19551,19568,19588,19610,19701],[23098,23291,23300,23317,23334,23350,23367,23383,23400,23416,23433,23450,23467,23517,23533,23550,23566,23583,23600,23616,23633,23650,23666,23683,23700,23716,23733,23750,23766,23783,23800,23816,23835,23883,23900,23917,23934,23950,23966,23983,24000,24017,24033,24050,24066,24083,24100,24116,24133,24150,24166,24183,24200,24216,24233,24254],[25224,25483,25500,25516,25533,25549,25566,25583,25599,25616,25633,25649,25666,25697,25733],[26608,26866,26883,26899,26916,26933,26949,26966,26982,26999,27016,27033,27049,27069,27083],[27832,28050,28066,28082,28099,28115,28133,28149,28166,28182,28199,28215,28232,28249,28265,28282,28299,28315,28332,28349,28365,28382,28399,28415,28432,28449,28465,28482,28499,28549,28568,28615,28632,28649,28665,28682,28699,28715,28732,28749,28765,28782,28799,28815,28832,28849,28866,28882,28902],[29914,30149,30165,30182,30198,30215,30232,30248,30265,30282,30298,30315,30331,30348,30365,30382,30398,30415,30432,30535,30550,30570,30582,30598,30615,30631,30648,30665,30681,30698,30715,30732,30748,30765,30781,30798,30815,30831,30848,30865,30881,30898,30915,30932,30948,30969,31083,31098,31115,31132,31148,31165,31181,31198,31215,31232,31248,31265,31288,31298,31315,31332,31353,31380,31398,31415,31432,31448,31465,31482,31498,31515,31531,31548,31565,31581,31598,31615,31631,31648,31665,31681,31698,31715,31731,31748,31764,31781,31798,31814,31835],[33656,33942,33947,33964,33981,33997,34014,34031,34047,34064,34080,34097,34114,34131,34147,34164,34181,34197,34214,34230,34247,34264,34280,34297,34315,34331,34347,34365,34380,34397,34414,34430,34447,34464,34480,34497,34514,34531,34547,34564,34580,34597,34613,34630,34648,34663,34680]],"version":"2.0.0"}.

True or False For any function f, and any real number c,limx→c-f(x)=limx→c+f(x).

What are the domain and range of f(x)=lnx?

Use a graphing utility to find the indicated limit rounded to two decimal places.

limx→-1x3+x2+3x+3x4+x3+2x+2

In Problems 7– 42, find each limit algebraically.

limx→0x2-4x2+4.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free