IDENTIFIKASI KESALAHAN MAHASISWA DALAM PENYELESAIAN SOAL-SOAL LIMIT

Budi Mulyono, Hapizah Hapizah

Abstract


Limit is a main topic of calculus studied especially by students of mathematics education. Despite the fact that limit has been introduced and taught to students at the level of senior high school, there are many student’s mistakes occured in student’s answers of limit questions. These findings came from results of survey of 73 students of mathematics education by giving them some questions of limit. The student’s mistakes of solving of limit questions that the researchers identify are that students consider limit questions could be solved if there is a kind of variables (for instance, variable ) in a function which its limit will be determined; that students consider the value of limit  as  is the result of substituting of variable  directly into the function ; that students are not aware of left-sided limit and right-sided when determining the value of limit of a function, and that students do not use appropriately all information in form of graphic of a function to determine the value of limit of the function.Limit is a main top Limit is a main topLimit is a main topLimit is a main topLimit is a main topLimit is a main topLimit is a main topLimit is a main topLimit is a main topLimit is a main topLimit is a main topLimit is a main top Limit is a main top Limit is a main topLimit is a main top ic of calculuic of calculu ic of calculuic of calculuic of calculuic of calculu ic of calculu ic of calculus studied especially studied especially studied especially studied especially studied especially studied especially studied especially studied especially studied especially studied especially studied especially by students of mathematics students of mathematics students of mathematics students of mathematics students of mathematics students of mathematics students of mathematics students of mathematics students of mathematics students of mathematics students of mathematics students of mathematics students of mathematics students of mathematics students of mathematics education. education. education. education. education. education. education. 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Despite the fact that limit has been introduced and taught to students at level of Despite the fact that limit has been introduced and taught to students at level of Despite the fact that limit has been introduced and taught to students at level of Despite the fact that limit has been introduced and taught to students at level of Despite the fact that limit has been introduced and taught to students at level of Despite the fact that limit has been introduced and taught to students at level of Despite the fact that limit has been introduced and taught to students at level of Despite the fact that limit has been introduced and taught to students at level of Despite the fact that limit has been introduced and taught to students at level of Despite the fact that limit has been introduced and taught to students at level of Despite the fact that limit has been introduced and taught to students at level of senior high school, senior high school, senior high school, senior high school, senior high school, senior high school, senior high school, senior high school, senior high school, senior high school, there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes there are many student’s mistakes occured occuredoccured in in student’s answers of student’s answers of student’s answers of student’s answers of student’s answers of student’s answers of student’s answers of student’s answers of student’s answers of student’s answers of student’s answers of limit limit limit limit limit limit questions. questions. questions. These These findings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education indings came from results of survey 73 students mathematics education by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that by giving them some questions of limit. The student’s mistakes solving limit that the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider the researchers identify are that students consider limit questions could be solvelimit questions could be solvelimit questions could be solvelimit questions could be solvelimit questions could be solvelimit questions could be solvelimit questions could be solve limit questions could be solve limit questions could be solvelimit questions could be solvelimit questions could be solve limit questions could be solve limit questions could be solve limit questions could be solvelimit questions could be solve limit questions could be solve limit questions could be solvelimit questions could be solve limit questions could be solve d if there is a d if there is a d if there is a d if there is a d if there is a d if there is a d if there is a d if there is a d if there is a d if there is a d if there is a d if there is a d if there is a kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable kind of variables (for instance, variable
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as
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; that ; that ; that ; that ; that ; that students are not students are not students are not students are not students are not students are not students are not students are not students are not students are not students are not students are not students are not awareawareaware of leftof leftof leftof leftof left of left-sided limit and right sided limit and right sided limit and rightsided limit and rightsided limit and rightsided limit and rightsided limit and rightsided limit and rightsided limit and rightsided limit and rightsided limit and rightsided limit and right sided limit and rightsided limit and rightsided limit and rightsided limit and right sided limit and right-sided sided sided sided when when when when determining the value of limit a function, and that students do not use appropriately all determining the value of limit a function, and that students do not use appropriately all determining the value of limit a function, and that students do not use appropriately all determining the value of limit a function, and that students do not use appropriately all determining the value of limit a function, and that students do not use appropriately all determining the value of limit a function, and that students do not use appropriately all determining the value of limit a function, and that students do not use appropriately all determining the value of limit a function, and that students do not use appropriately all determining the value of limit a function, and that students do not use appropriately all determining the value of limit a function, and that students do not use appropriately all determining the value of limit a function, and that students do not use approp

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