Pertanyaan

Jika f ( x ) = x 2 − 2 x − 13 nilai dari h → 0 lim h f ( x + h ) − f ( x ) adalah ....

Jika $f (x) = x^{2} - 2 x - 13$ nilai dari $h \to 0 lim \frac{f ( x + h ) - f ( x )}{h}$ adalah ....

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A. Acfreelance

Master Teacher

Mahasiswa/Alumni UIN Walisongo Semarang

Jawaban terverifikasi

Pembahasan

Mencari f(x+h) Subsitusi ke nilai lim Jadi hasil dari nilai dari = 2x -2

Mencari f(x+h)

Subsitusi ke nilai lim

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight h rightwards arrow 0 of fraction numerator straight f open parentheses straight x plus straight h close parentheses minus straight f open parentheses straight x close parentheses over denominator straight h end fraction end cell equals cell limit as h rightwards arrow 0 of fraction numerator open parentheses x squared plus 2 x h plus h squared minus 2 x minus 2 h minus 13 close parentheses minus open parentheses x squared minus 2 x minus 13 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator x squared plus 2 x h plus h squared minus 2 x minus 2 h minus 13 minus x squared plus 2 x plus 13 over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 x h plus h squared minus 2 h over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of 2 x plus h minus 2 end cell row blank equals cell 2 x minus 2 end cell end table$

Jadi hasil dari straight f left parenthesis straight x right parenthesis equals straight x squared minus 2 straight x minus 13 nilai dari $limit as straight h rightwards arrow 0 of fraction numerator straight f open parentheses straight x plus straight h close parentheses minus straight f open parentheses straight x close parentheses over denominator straight h end fraction$ = 2x -2