Roboguru

Diketahui :    Tentukan nilai limit  jika ada.

Pertanyaan

Diketahui : 

g open parentheses x close parentheses equals open curly brackets table attributes columnalign left end attributes row cell 3 minus x comma space jika space x greater or equal than 1 end cell row cell x squared comma space jika space x less than 1 end cell end table close 

Tentukan nilai limit g open parentheses x close parentheses jika ada. 

Pembahasan Soal:

Yang dimaksud soal adalah tentukan nilai limit g open parentheses x close parentheses di x equals 1 jika ada. 


Dikatakan nilai limit g open parentheses x close parentheses untuk x equals a ada jika dan hanya jika limit as x rightwards arrow a to the power of minus of f open parentheses x close parentheses equals limit as x rightwards arrow a to the power of plus of f open parentheses x close parentheses

Diketahui 

g open parentheses x close parentheses equals open curly brackets table attributes columnalign left end attributes row cell 3 minus x comma space jika space x greater or equal than 1 end cell row cell x squared comma space jika space x less than 1 end cell end table close 

Maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 to the power of minus of g open parentheses x close parentheses end cell equals cell limit as x rightwards arrow 1 to the power of minus of open parentheses x squared close parentheses end cell row blank equals cell open parentheses 1 close parentheses squared end cell row blank equals 1 row blank blank blank row cell limit as x rightwards arrow 1 to the power of plus of g open parentheses x close parentheses end cell equals cell limit as x rightwards arrow 1 to the power of minus of open parentheses 3 minus x close parentheses end cell row blank equals cell 3 minus open parentheses 1 close parentheses end cell row blank equals 2 end table 

Karena limit as x rightwards arrow 1 to the power of minus of g open parentheses x close parentheses not equal to limit as x rightwards arrow 1 to the power of plus of g open parentheses x close parentheses, maka nilai limit g open parentheses x close parentheses untuk x equals 1 tidak ada. 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Mei 2021

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