Pertanyaan

Nilai x → ∞ lim ( 2 x − 4 x 2 + x + 3 ) adalah ....

Nilai $x \to \infty lim (2 x - 4 x^{2} + x + 3)$ adalah ....

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style bold i bold right parenthesis bold space Rasionalkan space bentuk space limit space di space atas limit as straight x rightwards arrow straight infinity of invisible function application space open parentheses 2 straight x minus square root of 4 straight x squared plus straight x plus 3 end root close parentheses equals limit as straight x rightwards arrow straight infinity of invisible function application space open parentheses 2 straight x minus square root of 4 straight x squared plus straight x plus 3 end root close parentheses. fraction numerator 2 straight x plus square root of 4 straight x squared plus straight x plus 3 end root over denominator 2 straight x plus square root of 4 straight x squared plus straight x plus 3 end root end fraction equals limit as straight x rightwards arrow straight infinity of invisible function application space fraction numerator open parentheses 2 straight x close parentheses squared minus open parentheses square root of 4 straight x squared plus straight x plus 3 end root close parentheses squared over denominator 2 straight x plus square root of 4 straight x squared plus straight x plus 3 end root end fraction equals limit as straight x rightwards arrow straight infinity of invisible function application space fraction numerator 4 straight x squared minus open parentheses 4 straight x squared plus straight x plus 3 close parentheses over denominator 2 straight x plus square root of 4 straight x squared plus straight x plus 3 end root end fraction equals limit as straight x rightwards arrow straight infinity of invisible function application space fraction numerator negative straight x minus 3 over denominator 2 straight x plus square root of 4 straight x squared plus straight x plus 3 end root end fraction bold ii bold right parenthesis bold space Gunakan space sifat space limit space di space ketakhinggaan box enclose limit as straight x rightwards arrow straight infinity of invisible function application space 1 over straight x to the power of straight p equals 0 space untuk space straight p greater than 0 end enclose limit as straight x rightwards arrow straight infinity of invisible function application space fraction numerator negative straight x minus 3 over denominator 2 straight x plus square root of 4 straight x squared plus straight x plus 3 end root end fraction equals limit as straight x rightwards arrow straight infinity of invisible function application space fraction numerator negative straight x minus 3 over denominator 2 straight x plus square root of 4 straight x squared plus straight x plus 3 end root end fraction. fraction numerator 1 over straight x over denominator 1 over straight x end fraction equals limit as straight x rightwards arrow straight infinity of invisible function application space fraction numerator negative 1 minus 3 over straight x over denominator 2 plus square root of 4 plus 1 over straight x plus 3 over straight x squared end root end fraction equals fraction numerator negative 1 minus 0 over denominator 2 plus square root of 4 plus 0 plus 0 end root end fraction equals fraction numerator negative 1 over denominator 2 plus 2 end fraction equals negative 1 fourth bold iii bold right parenthesis space Tambahan space colon box enclose limit as straight x rightwards arrow straight infinity of invisible function application space square root of ax squared plus bx plus straight c end root minus square root of px squared plus qx plus straight r end root equals fraction numerator straight b minus straight q over denominator 2 square root of straight a end fraction jika space straight a equals straight p end enclose Karena space limit as straight x rightwards arrow straight infinity of invisible function application space 2 straight x minus square root of 4 straight x squared plus straight x plus 3 end root equals limit as straight x rightwards arrow straight infinity of invisible function application space square root of 4 straight x squared end root minus square root of 4 straight x squared plus straight x plus 3 end root Dengan space straight a equals 4 comma space straight b equals 0 comma space straight c equals 0 comma space straight p equals 4 comma space straight q equals 1 comma space straight r equals 3 comma space sehingga space straight p equals straight q comma space maka limit as straight x rightwards arrow straight infinity of invisible function application space square root of 4 straight x squared end root minus square root of 4 straight x squared plus straight x plus 3 end root equals fraction numerator 0 minus 1 over denominator 2 square root of 4 end fraction equals fraction numerator negative 1 over denominator 2.2 end fraction equals negative 1 fourth end style$

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