Pertanyaan

Tentukan nilai limit fungsi berikut. 8. x → 1 lim 5 x 3 x 3 − 4 x 2 + 10 x

Tentukan nilai limit fungsi berikut.

$8. x \to 1 lim \frac{3 x ^{3} - 4 x ^{2} + 10 x}{5 x}$

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Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x cubed minus 4 x squared plus 10 x over denominator 5 x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 9 over 5 end cell end table end style$ .

Pembahasan

Diketahui: Pembagian limit fungsi. Substitusi variabel dengan pada fungsi seperti berikut: Jadi, nilai dari .

Diketahui:

Pembagian limit fungsi.

Substitusi variabel begin mathsize 14px style x end style dengan begin mathsize 14px style 1 end style pada fungsi seperti berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of space fraction numerator 3 x cubed minus 4 x squared plus 10 x over denominator 5 x end fraction end cell equals cell fraction numerator 3 open parentheses 1 close parentheses cubed minus 4 open parentheses 1 close parentheses squared plus 10 open parentheses 1 close parentheses over denominator 5 open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator 3 minus 4 plus 10 over denominator 5 end fraction end cell row blank equals cell 9 over 5 end cell end table end style$

Jadi, nilai dari $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x cubed minus 4 x squared plus 10 x over denominator 5 x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 9 over 5 end cell end table end style$ .