Pertanyaan

h → 0 lim h 4 − h 2 tan ( − x + h ) − tan ( − x − h ) = ...

$h \to 0 lim \frac{tan ( - x + h ) - tan ( - x - h )}{h 4 - h ^{2}} = ...$

sec x
2 sec x

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style Gunakan space aturan space straight L apostrophe Hospital limit as straight h rightwards arrow 0 of space fraction numerator tan left parenthesis negative straight x plus straight h right parenthesis minus tan left parenthesis negative straight x minus straight h right parenthesis over denominator straight h square root of 4 minus straight h squared end root end fraction equals limit as straight h rightwards arrow 0 of space fraction numerator 1 over denominator straight h square root of 4 minus straight h squared end root end fraction. limit as straight h rightwards arrow 0 of space fraction numerator tan left parenthesis negative straight x plus straight h right parenthesis minus tan left parenthesis negative straight x minus straight h right parenthesis over denominator straight h end fraction equals fraction numerator 1 over denominator square root of 4 minus 0 squared end root end fraction. limit as straight h rightwards arrow 0 of space fraction numerator sec squared left parenthesis negative straight x plus straight h right parenthesis plus sec squared left parenthesis negative straight x minus straight h right parenthesis over denominator 1 end fraction equals fraction numerator 1 over denominator square root of 4 end fraction. limit as straight h rightwards arrow 0 of space sec squared left parenthesis negative straight x plus straight h right parenthesis plus sec squared left parenthesis negative straight x minus straight h right parenthesis equals 1 half space left parenthesis sec squared left parenthesis negative straight x right parenthesis plus sec squared left parenthesis negative straight x right parenthesis right parenthesis equals 1 half space 2 space sec squared left parenthesis negative straight x right parenthesis equals sec squared left parenthesis negative straight x right parenthesis equals sec squared space straight x end style$