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Diketahui dan Jika , maka nilai dari adalah ....

Diketahui begin mathsize 14px style limit as x rightwards arrow 2 of invisible function application f open parentheses x close parentheses equals 7 end style dan limit as x rightwards arrow 2 of invisible function application g open parentheses x close parentheses equals negative 2. Jika begin mathsize 14px style limit as x rightwards arrow 2 of invisible function application fraction numerator f open parentheses x close parentheses plus g open parentheses x close parentheses over denominator p times f open parentheses x close parentheses times g open parentheses x close parentheses end fraction equals 25 end style, maka nilai dari begin mathsize 14px style limit as x rightwards arrow 2 of left parenthesis f open parentheses x close parentheses plus 2 g open parentheses x close parentheses right parenthesis to the power of 70 p end exponent end style adalah ....

  1. begin mathsize 14px style 9 end style

  2. begin mathsize 14px style 3 end style

  3. begin mathsize 14px style 1 end style

  4. begin mathsize 14px style 1 over 9 end style

  5. size 14px 1 over size 14px 3

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

jawaban yang tepat adalah E.

Pembahasan

Perhatikan perhitungan berikut! Dengan demikian, nilai dari dapat dihitung sebagai berikut. Jadi, jawaban yang tepat adalah E.

Perhatikan perhitungan berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator f open parentheses x close parentheses plus g open parentheses x close parentheses over denominator p times f open parentheses x close parentheses times g open parentheses x close parentheses end fraction end cell equals 25 row cell fraction numerator limit as x rightwards arrow 2 of open parentheses f open parentheses x close parentheses plus g open parentheses x close parentheses close parentheses over denominator limit as x rightwards arrow 2 of open parentheses p times f open parentheses x close parentheses times g open parentheses x close parentheses close parentheses end fraction end cell equals 25 row cell fraction numerator limit as x rightwards arrow 2 of f open parentheses x close parentheses plus limit as x rightwards arrow 2 of g open parentheses x close parentheses over denominator limit as x rightwards arrow 2 of p times limit as x rightwards arrow 2 of f open parentheses x close parentheses times limit as x rightwards arrow 2 of g open parentheses x close parentheses end fraction end cell equals 25 row cell fraction numerator 7 plus open parentheses negative 2 close parentheses over denominator p times 7 times open parentheses negative 2 close parentheses end fraction end cell equals 25 row cell fraction numerator 5 over denominator negative 14 p end fraction end cell equals 25 row cell fraction numerator 1 over denominator negative 14 p end fraction end cell equals 5 row cell negative 14 p end cell equals cell 1 fifth end cell row p equals cell negative 1 over 70 end cell end table end style

Dengan demikian, nilai dari begin mathsize 14px style limit as x rightwards arrow 2 of left parenthesis f open parentheses x close parentheses plus 2 g open parentheses x close parentheses right parenthesis to the power of 70 p end exponent end style dapat dihitung sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px left parenthesis size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 2 size 14px g begin mathsize 14px style left parenthesis x right parenthesis end style size 14px right parenthesis to the power of size 14px 70 size 14px p end exponent end cell row blank size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below begin mathsize 14px style left parenthesis f open parentheses x close parentheses plus 2 g open parentheses x close parentheses right parenthesis end style to the power of size 14px 70 begin mathsize 14px style open parentheses negative 1 over 70 close parentheses end style end exponent end cell row blank size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below begin mathsize 14px style left parenthesis f open parentheses x close parentheses plus 2 g open parentheses x close parentheses right parenthesis end style to the power of size 14px minus size 14px 1 end exponent end cell row blank size 14px equals cell begin mathsize 14px style open parentheses limit as x rightwards arrow 2 of open parentheses f open parentheses x close parentheses plus 2 g open parentheses x close parentheses close parentheses close parentheses end style to the power of negative 1 end exponent end cell row blank size 14px equals cell begin mathsize 14px style open parentheses limit as x rightwards arrow 2 of f open parentheses x close parentheses plus limit as x rightwards arrow 2 of open parentheses 2 g open parentheses x close parentheses close parentheses close parentheses end style to the power of negative 1 end exponent end cell row blank size 14px equals cell begin mathsize 14px style open parentheses limit as x rightwards arrow 2 of f open parentheses x close parentheses plus 2 limit as x rightwards arrow 2 of g open parentheses x close parentheses close parentheses end style to the power of negative 1 end exponent end cell row blank size 14px equals cell begin mathsize 14px style left parenthesis 7 plus 2 open parentheses negative 2 close parentheses right parenthesis end style to the power of negative 1 end exponent end cell row blank size 14px equals cell begin mathsize 14px style left parenthesis 7 minus 4 right parenthesis end style to the power of negative 1 end exponent end cell row blank size 14px equals cell size 14px 3 to the power of negative 1 end exponent end cell row blank size 14px equals cell size 14px 1 over size 14px 3 end cell end table

Jadi, jawaban yang tepat adalah E.

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