Pertanyaan

Jika x → a lim x − a f ( x 3 ) − f ( a 3 ) = − 1 , maka f'(1) = ....

Jika $x \to a lim \frac{f ( x ^{3} ) - f ( a ^{3} )}{x - a} = - 1$ , maka f'(1) = ....

-1
1
2

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Pembahasan

$begin mathsize 14px style Dengan space menggunakan space dalil space straight L ’ Hospital space diperoleh colon limit as straight x rightwards arrow straight a of invisible function application fraction numerator straight f apostrophe open parentheses straight x cubed close parentheses straight space. straight space 3 straight x squared over denominator 1 end fraction equals negative 1 straight f apostrophe open parentheses straight a cubed close parentheses straight space. straight space 3 straight a squared equals negative 1 straight f apostrophe open parentheses straight a cubed close parentheses equals negative fraction numerator 1 over denominator 3 straight a squared end fraction Karena space yang space diminta space adalah space straight f apostrophe left parenthesis 1 right parenthesis comma space maka straight a cubed equals 1 straight a equals 1 Substitusikan space kembali space ke space persamaan space di space atas colon straight f apostrophe space open parentheses 1 close parentheses equals negative fraction numerator 1 over denominator 3 open parentheses 1 close parentheses squared end fraction equals negative 1 third end style$