L4 Limits at Infinity - Practice 3
Completion requirements
Unit 1B
Limits
Lesson 4: Limits at Infinity
Practice
Once you feel confident with additional limits at infinity problems, click on the Practice tab and complete problem 1. Check your answers by going to the Solutions tab.
Instructions: Click the Download File button to download a printable PDF of the questions. Answer each of the following practice questions on a separate piece of paper. Step by step solutions are provided under the Solutions tab. You will learn the material more thoroughly if you complete the questions before checking the answers.
Instructions: Click the Download File button to download a printable PDF of the questions. Answer each of the following practice questions on a separate piece of paper. Step by step solutions are provided under the Solutions tab. You will learn the material more thoroughly if you complete the questions before checking the answers.
1.
Sketch a possible graph for a function with the following properties.
«math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mn»0«/mn»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mn»4«/mn»«mspace linebreak=¨newline¨/»«mspace
linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»0«/mn»«mo»§#8722;«/mo»«/msup»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mn»5«/mn»«mspace
linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»0«/mn»«mo»+«/mo»«/msup»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mn»1«/mn»«mspace
linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8722;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mo»§#8722;«/mo»«mo»§#8734;«/mo»«mspace
linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mn»6«/mn»«mspace
linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»5«/mn»«mo»§#8722;«/mo»«/msup»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mo»§#8722;«/mo»«mo»§#8734;«/mo»«mspace
linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»5«/mn»«mo»+«/mo»«/msup»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mo»§#8734;«/mo»«/mstyle»«/math»
1.
Sketch a possible graph for a function with the following properties.
«math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mn»0«/mn»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mn»4«/mn»«mspace linebreak=¨newline¨/»«mspace
linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»0«/mn»«mo»§#8722;«/mo»«/msup»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mn»5«/mn»«mspace
linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»0«/mn»«mo»+«/mo»«/msup»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mn»1«/mn»«mspace
linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8722;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mo»§#8722;«/mo»«mo»§#8734;«/mo»«mspace
linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mn»6«/mn»«mspace
linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»5«/mn»«mo»§#8722;«/mo»«/msup»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mo»§#8722;«/mo»«mo»§#8734;«/mo»«mspace
linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»5«/mn»«mo»+«/mo»«/msup»«/mrow»«/munder»«mi»f«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«mo»=«/mo»«mo»§#8734;«/mo»«/mstyle»«/math»
