Pertanyaan

h → 0 lim h 4 x + 4 h − 4 x

$h \to 0 lim \frac{4 x + 4 h - 4 x}{h}$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Limit mendekati sama dengan , ditulis: jika untuk setiap yang cukup dekat dengan tetapi , mendekati .

Limit mendekati sama dengan , ditulis:

jika untuk setiap yang cukup dekat dengan tetapi , mendekati .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as h rightwards arrow 0 of space fraction numerator square root of 4 x plus 4 h end root minus square root of 4 x end root over denominator h end fraction end cell equals cell limit as h rightwards arrow 0 of space fraction numerator square root of 4 x plus 4 h end root minus square root of 4 x end root over denominator h end fraction cross times fraction numerator square root of 4 x plus 4 h end root plus square root of 4 x end root over denominator square root of 4 x plus 4 h end root plus square root of 4 x end root end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator open parentheses 4 x plus 4 h close parentheses minus 4 x over denominator h open parentheses square root of 4 x plus 4 h end root plus square root of 4 x end root close parentheses end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator 4 x plus 4 h minus 4 x over denominator h open parentheses square root of 4 x plus 4 h end root plus square root of 4 x end root close parentheses end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator 4 h over denominator h open parentheses square root of 4 x plus 4 h end root plus square root of 4 x end root close parentheses end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator 4 over denominator open parentheses square root of 4 x plus 4 h end root plus square root of 4 x end root close parentheses end fraction end cell row blank equals cell fraction numerator 4 over denominator open parentheses square root of 4 x plus 4 left parenthesis 0 right parenthesis end root plus square root of 4 x end root close parentheses end fraction end cell row blank equals cell fraction numerator 4 over denominator square root of 4 x end root plus square root of 4 x end root end fraction end cell row blank equals cell fraction numerator 4 over denominator 2 square root of 4 x end root end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 4 x end root end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 4 x end root end fraction cross times fraction numerator square root of 4 x end root over denominator square root of 4 x end root end fraction end cell row blank equals cell fraction numerator 2 square root of 4 x end root over denominator 4 x end fraction end cell row blank equals cell fraction numerator 2 cross times 2 square root of x over denominator 4 x end fraction end cell row blank equals cell fraction numerator 4 square root of x over denominator 4 x end fraction end cell row blank equals cell fraction numerator square root of x over denominator x end fraction end cell row blank blank blank end table end style$