Pertanyaan

Tentukan h → 0 lim h f ( x + h ) − f ( x ) dari fungsi f ( x ) = x 2 + 2 .

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

A. Fatta

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

dari fungsi adalah .

$limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction$ dari fungsi

f open parentheses x close parentheses equals x squared plus 2

adalah

Pembahasan

Diketahui fungsi , maka Sehingga, Jadi, dari fungsi adalah .

Diketahui fungsi f open parentheses x close parentheses equals x squared plus 2 , maka

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x plus h close parentheses end cell equals cell open parentheses x plus h close parentheses squared plus 2 end cell row blank equals cell x squared plus 2 x h plus h squared plus 2 end cell end table

Sehingga,

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

Jadi, $limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction$ dari fungsi adalah 2 x .