Pertanyaan

Diketahui f ( x ) = 2 x 3 . Tentukan nilai dari h → 0 lim h f ( x + h ) − f ( x ) .

Diketahui $f (x) = 2 x^{3}$ . Tentukan nilai dari $h \to 0 lim \frac{f ( x + h ) - f ( x )}{h}$ .

M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari $begin mathsize 14px style limit as h rightwards arrow 0 of space fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction equals 6 x squared end style$ .

Pembahasan

Diketahui: Fungsi Ditanya:Tentukan nilai dari ! Jawab: Ingat bagaimana cara menentukan nilai limit dengan cara substitusi.Perhatikan perhitungan berikut. Jadi,nilai dari .

Diketahui: Fungsi begin mathsize 14px style f open parentheses x close parentheses equals 2 x cubed end style

Ditanya: Tentukan nilai dari $begin mathsize 14px style limit as h rightwards arrow 0 of space fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction end style$ !

Jawab:

Ingat bagaimana cara menentukan nilai limit dengan cara substitusi. Perhatikan perhitungan berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as h rightwards arrow 0 of space fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction end cell equals cell limit as h rightwards arrow 0 of space fraction numerator 2 open parentheses x plus h close parentheses cubed minus 2 x cubed over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator 2 open parentheses x cubed plus 3 x squared h plus 3 x h squared plus h cubed close parentheses minus 2 x cubed over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator 2 x cubed plus 6 x squared h plus 6 x h squared plus 2 h cubed minus 2 x cubed over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator 2 x cubed minus 2 x cubed plus 6 x squared h plus 6 x h squared plus 2 h cubed over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator 6 x squared h plus 6 x h squared plus 2 h cubed over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator h left parenthesis 6 x squared plus 6 x h plus 2 h squared right parenthesis over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator up diagonal strike h left parenthesis 6 x squared plus 6 x h plus 2 h squared right parenthesis over denominator up diagonal strike h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space 6 x squared plus 6 x h plus 2 h squared end cell row blank equals cell space 6 x squared plus 6 x left parenthesis 0 right parenthesis plus 2 left parenthesis 0 right parenthesis squared space equals 6 x squared plus 0 plus 0 end cell row blank equals cell 6 x squared end cell end table$

Jadi, nilai dari $begin mathsize 14px style limit as h rightwards arrow 0 of space fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction equals 6 x squared end style$ .

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