Pertanyaan

x → a lim ​ 2 x − 1 2 x 2 − 5 x + 14 ​ = 4 , nilai ayang memenuhi adalah ...

, nilai a yang memenuhi adalah ... 

A. Damanhuri

Master Teacher

Jawaban terverifikasi

Jawaban

.

 begin mathsize 14px style a equals 9 over 2 text atau end text space a equals 2 end style.

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Pembahasan

Substitusi Jadi, .

Substitusi begin mathsize 14px style x equals a end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight a of fraction numerator 2 x squared minus 5 x plus 14 over denominator 2 x minus 1 end fraction end cell equals 4 row cell fraction numerator 2 a squared minus 5 a plus 14 over denominator 2 a minus 1 end fraction end cell equals 4 row cell 2 a squared minus 5 a plus 14 end cell equals cell 4 left parenthesis 2 a minus 1 right parenthesis end cell row cell 2 a squared minus 5 a plus 14 end cell equals cell 8 a minus 4 end cell row cell 2 a squared minus 5 a plus 14 minus left parenthesis 8 a minus 4 right parenthesis end cell equals 0 row cell 2 a squared minus 13 a plus 18 end cell equals 0 row cell left parenthesis 2 a minus 9 right parenthesis left parenthesis a minus 2 right parenthesis end cell equals 0 row cell a subscript 1 end cell equals cell 9 over 2 logical or a subscript 2 equals 2 end cell row blank blank blank row blank blank blank row blank blank blank row blank blank blank end table end style

 

Jadi, begin mathsize 14px style a equals 9 over 2 text atau end text space a equals 2 end style.

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