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Pertanyaan

Tentukan nilai limit fungsi berikut.

a. limit as x rightwards arrow 0 of fraction numerator 2 x minus tan open parentheses 4 x close parentheses over denominator x plus sin open parentheses 3 x close parentheses end fraction 

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x minus tan open parentheses 4 x close parentheses over denominator x plus sin open parentheses 3 x close parentheses end fraction end cell end table equals negative 1 half.

Pembahasan

Substitusi langsung:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator 2 x minus tan open parentheses 4 x close parentheses over denominator x plus sin open parentheses 3 x close parentheses end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator 0 minus tan open parentheses 0 close parentheses over denominator 0 plus sin open parentheses 0 close parentheses end fraction end cell row blank equals cell 0 over 0 open parentheses tak space tentu close parentheses end cell end table

Membagi dengan x spacemaka diperoleh,

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator 2 x minus tan open parentheses 4 x close parentheses over denominator x plus sin open parentheses 3 x close parentheses end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator 2 x minus tan open parentheses 4 x close parentheses over denominator x plus sin open parentheses 3 x close parentheses end fraction cross times fraction numerator begin display style bevelled 1 over x end style over denominator begin display style bevelled 1 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator begin display style fraction numerator 2 x over denominator x end fraction end style minus begin display style fraction numerator tan open parentheses 4 x close parentheses over denominator x end fraction end style over denominator begin display style x over x end style plus begin display style fraction numerator sin open parentheses 3 x close parentheses over denominator x end fraction end style end fraction end cell row blank equals cell fraction numerator 2 minus 4 over denominator 1 plus 3 end fraction end cell row blank equals cell negative 1 half end cell end table

Dengan demikian, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x minus tan open parentheses 4 x close parentheses over denominator x plus sin open parentheses 3 x close parentheses end fraction end cell end table equals negative 1 half.

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