Pertanyaan

x → 1 lim 7 x 2 + 2 x − 11 x 2 − 2 x 3 x 2 + x − 5 x 2 − x = ...

$x \to 1 lim \frac{3 x ^{2} + x - 5 x ^{2} - x}{7 x ^{2} + 2 x - 11 x ^{2} - 2 x} =$ ...

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Nilai dari karena masih dilanjutkan menggunakan metode turunan fungsi aljabar Jadi, nilai dari

Nilai dari $limit as x rightwards arrow 1 of space fraction numerator square root of 3 x squared plus square root of x end root minus square root of 5 x squared minus square root of x end root over denominator square root of 7 x squared plus 2 square root of x end root minus square root of 11 x squared minus 2 square root of x end root end fraction$

$limit as x rightwards arrow 1 of space fraction numerator square root of 3 x squared plus square root of x end root minus square root of 5 x squared minus square root of x end root over denominator square root of 7 x squared plus 2 square root of x end root minus square root of 11 x squared minus 2 square root of x end root end fraction equals fraction numerator square root of 3 open parentheses 1 close parentheses squared plus square root of 1 end root minus square root of 5 open parentheses 1 close parentheses squared minus square root of 1 end root over denominator square root of 7 open parentheses 1 close parentheses squared plus 2 square root of 1 end root minus square root of 11 open parentheses 1 close parentheses squared minus 2 square root of 1 end root end fraction equals fraction numerator square root of 3 plus 1 end root minus square root of 5 minus 1 end root over denominator square root of 7 plus 2 end root minus square root of 11 minus 2 end root end fraction equals fraction numerator square root of 4 minus square root of 4 over denominator square root of 9 minus square root of 9 end fraction equals 0 over 0$

karena masih 0 over 0 dilanjutkan menggunakan metode turunan fungsi aljabar

$limit as x rightwards arrow 1 of fraction numerator square root of 3 x squared plus square root of x end root minus square root of 5 x squared minus square root of x end root over denominator square root of 7 x squared plus 2 square root of x end root minus square root of 11 x squared minus 2 square root of x end root end fraction limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x squared plus x to the power of begin display style 1 half end style end exponent close parentheses to the power of begin display style 1 half end style end exponent minus open parentheses 5 x squared minus x to the power of 1 half end exponent close parentheses to the power of 1 half end exponent over denominator open parentheses 7 x squared plus 2 x to the power of 1 half end exponent close parentheses to the power of 1 half end exponent minus open parentheses 11 x squared minus 2 x to the power of 1 half end exponent close parentheses to the power of 1 half end exponent end fraction limit as x rightwards arrow 1 of fraction numerator begin display style 1 half end style open parentheses 3 x squared plus x to the power of begin display style 1 half end style end exponent close parentheses to the power of begin display style negative 1 half end style end exponent open parentheses 6 x plus begin display style 1 half end style x to the power of negative begin display style 1 half end style end exponent close parentheses minus 1 half open parentheses 5 x squared minus x to the power of 1 half end exponent close parentheses to the power of negative 1 half end exponent open parentheses 10 x minus 1 half x to the power of negative begin display style 1 half end style end exponent close parentheses over denominator 1 half open parentheses 7 x squared plus 2 x to the power of 1 half end exponent close parentheses to the power of negative 1 half end exponent open parentheses 14 x plus x to the power of negative 1 half end exponent close parentheses minus 1 half open parentheses 11 x squared minus 2 x to the power of 1 half end exponent close parentheses to the power of negative 1 half end exponent open parentheses 22 x minus x to the power of negative 1 half end exponent close parentheses end fraction limit as x rightwards arrow 1 of fraction numerator begin display style 1 half end style over denominator begin display style 1 half end style end fraction times fraction numerator begin display style open parentheses open parentheses 3 x squared plus x to the power of fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction end exponent close parentheses to the power of negative fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction end exponent open parentheses 6 x plus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction x to the power of negative fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction end exponent close parentheses minus open parentheses 5 x squared minus x to the power of fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction end exponent close parentheses to the power of negative fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction end exponent open parentheses 10 x minus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction x to the power of negative fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction end exponent close parentheses close parentheses end style over denominator open parentheses open parentheses 7 x squared plus 2 x to the power of 1 half end exponent close parentheses to the power of negative 1 half end exponent open parentheses 14 x plus x to the power of negative 1 half end exponent close parentheses minus open parentheses 11 x squared minus 2 x to the power of 1 half end exponent close parentheses to the power of negative 1 half end exponent open parentheses 22 x minus x to the power of negative 1 half end exponent close parentheses close parentheses end fraction limit as x rightwards arrow 1 of fraction numerator begin display style open parentheses 3 x squared plus x to the power of 1 half end exponent close parentheses to the power of negative 1 half end exponent open parentheses 6 x plus 1 half x to the power of negative 1 half end exponent close parentheses minus 1 half open parentheses 5 x squared minus x to the power of 1 half end exponent close parentheses to the power of negative 1 half end exponent open parentheses 10 x minus 1 half x to the power of negative 1 half end exponent close parentheses end style over denominator open parentheses 7 x squared plus 2 x to the power of 1 half end exponent close parentheses to the power of negative 1 half end exponent open parentheses 14 x plus x to the power of negative 1 half end exponent close parentheses minus 1 half open parentheses 11 x squared minus 2 x to the power of 1 half end exponent close parentheses to the power of negative 1 half end exponent open parentheses 22 x minus x to the power of negative 1 half end exponent close parentheses end fraction limit as x rightwards arrow 1 of fraction numerator begin display style fraction numerator 1 over denominator square root of 3 x squared plus square root of x end root end fraction end style open parentheses 6 x plus begin display style fraction numerator 1 over denominator 2 square root of x end fraction end style close parentheses minus space fraction numerator 1 over denominator square root of 5 x squared plus square root of x end root end fraction open parentheses 10 x minus fraction numerator 1 over denominator 2 square root of x end fraction close parentheses over denominator fraction numerator 1 over denominator square root of 7 x squared plus square root of x end root end fraction open parentheses 14 x plus fraction numerator 1 over denominator square root of x end fraction close parentheses minus fraction numerator 1 over denominator square root of 11 x squared plus square root of x end root end fraction open parentheses 22 x minus fraction numerator 1 over denominator square root of x end fraction close parentheses end fraction substitusi space straight x equals 1 space ke space persamaan space yang space telah space diturunkan equals fraction numerator begin display style fraction numerator 1 over denominator square root of 3 left parenthesis 1 right parenthesis squared plus square root of 1 end root end root end fraction open parentheses 6 left parenthesis 1 right parenthesis plus fraction numerator 1 over denominator 2 square root of 1 end fraction close parentheses minus space fraction numerator 1 over denominator square root of 5 left parenthesis 1 right parenthesis squared plus square root of 1 end root end root end fraction open parentheses 10 left parenthesis 1 right parenthesis minus fraction numerator 1 over denominator 2 square root of 1 end fraction close parentheses end style over denominator fraction numerator 1 over denominator square root of 7 left parenthesis 1 right parenthesis squared plus square root of 1 end root end root end fraction open parentheses 14 left parenthesis 1 right parenthesis plus fraction numerator 1 over denominator square root of 1 end fraction close parentheses minus fraction numerator 1 over denominator square root of 11 left parenthesis 1 right parenthesis squared plus square root of 1 end root end root end fraction open parentheses 22 left parenthesis 1 right parenthesis minus fraction numerator 1 over denominator square root of 1 end fraction close parentheses end fraction equals fraction numerator begin display style fraction numerator 1 over denominator square root of 4 end fraction end style open parentheses 6 plus begin display style 1 half end style close parentheses minus fraction numerator 1 over denominator square root of 4 end fraction open parentheses 10 minus 1 half close parentheses over denominator fraction numerator 1 over denominator square root of 9 end fraction open parentheses 14 plus 1 close parentheses minus fraction numerator 1 over denominator square root of 9 end fraction open parentheses 22 minus 1 close parentheses end fraction equals fraction numerator begin display style 1 half end style open parentheses begin display style 13 over 2 end style close parentheses minus begin display style 1 half end style open parentheses begin display style 19 over 2 end style close parentheses over denominator begin display style 1 third end style left parenthesis 15 right parenthesis minus begin display style 1 third end style left parenthesis 21 right parenthesis end fraction equals fraction numerator begin display style 13 over 4 end style minus begin display style 19 over 4 end style over denominator 5 minus 7 end fraction equals fraction numerator negative begin display style 6 over 4 end style over denominator negative 2 end fraction equals 3 over 4$

Jadi, nilai dari $limit as x rightwards arrow 1 of space fraction numerator square root of 3 x squared plus square root of x end root minus square root of 5 x squared minus square root of x end root over denominator square root of 7 x squared plus 2 square root of x end root minus square root of 11 x squared minus 2 square root of x end root end fraction equals 3 over 4$

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