Pertanyaan

Jika f ( x ) = 5 x 3 + 7 x 2 maka nilai x → 0 lim h f ( x + h ) − f ( x ) adalah ....

Jika $f (x) = 5 x^{3} + 7 x^{2}$ maka nilai $x \to 0 lim \frac{f ( x + h ) - f ( x )}{h}$ adalah ....

N. Sari

Master Teacher

Mahasiswa/Alumni Universitas Nasional

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B

Pembahasan

Berdasarkan sifat limit, maka didapatkan : Maka nilai adalah Oleh karena itu,jawaban yang benar adalah B

Berdasarkan sifat limit, maka didapatkan :

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f left parenthesis x right parenthesis over denominator h end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator 5 open parentheses x plus h close parentheses cubed plus 7 open parentheses x plus h close parentheses squared minus left parenthesis 5 x cubed plus 7 x squared right parenthesis over denominator h end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 5 open parentheses x cubed plus 3 x squared h plus 3 x h squared plus h cubed close parentheses plus 7 open parentheses x squared plus 2 x h plus h squared close parentheses minus 5 x cubed minus 7 x squared over denominator h end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 5 x cubed plus 15 x squared h plus 15 x h squared plus 5 h cubed plus 7 x squared plus 14 x h plus 7 h squared minus 5 x cubed minus 7 x squared over denominator h end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 5 x cubed minus 5 x cubed plus 7 x squared minus 7 x squared plus 5 h cubed plus 7 h squared plus 15 x h squared plus 15 x squared h plus 14 x h over denominator h end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator h left parenthesis 5 h squared plus 7 h plus 15 x h plus 15 x squared plus 14 x right parenthesis over denominator h end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space 5 h squared plus 7 h plus 15 x h plus 15 x squared plus 14 x end cell row blank equals cell 5 left parenthesis 0 right parenthesis squared plus 7 left parenthesis 0 right parenthesis plus 15 x left parenthesis 0 right parenthesis plus 15 x squared plus 14 x end cell row blank equals cell 15 x squared plus 14 x end cell end table$

Maka nilai $limit as x rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f left parenthesis x right parenthesis over denominator h end fraction$ adalah Error converting from MathML to accessible text.

Oleh karena itu, jawaban yang benar adalah B