Roboguru

Selesaikanlah. c. x→0lim​3x5+6x2(3x−1)5(2x+5)2​

Pertanyaan

Selesaikanlah.

c. begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator open parentheses 3 x minus 1 close parentheses to the power of 5 open parentheses 2 x plus 5 close parentheses squared over denominator 3 x to the power of 5 plus 6 x squared end fraction end style 

Pembahasan:

Ingat aturan berikut !

limit as x rightwards arrow a minus of f open parentheses x close parentheses equals limit as x rightwards arrow a plus of f open parentheses x close parentheses equals L space dan thin space limit as x rightwards arrow a of f open parentheses x close parentheses equals L

Maka,

begin mathsize 12px style limit as x rightwards arrow thin space 0 minus of open parentheses fraction numerator open parentheses 3 x minus 1 close parentheses to the power of 5 open parentheses 2 x plus 5 close parentheses squared over denominator 3 x to the power of 5 plus 6 x squared end fraction close parentheses equals limit as x rightwards arrow thin space 0 minus of open parentheses open parentheses 3 x minus 1 close parentheses to the power of 5 open parentheses 2 x plus 5 close parentheses squared open parentheses 3 x to the power of 5 plus 6 x squared close parentheses to the power of negative 1 end exponent close parentheses end style

 

Karena limit as x rightwards arrow a of open square brackets f left parenthesis x right parenthesis times g left parenthesis x right parenthesis close square brackets equals limit as x rightwards arrow a of f left parenthesis x right parenthesis times limit as x rightwards arrow a of g left parenthesis x right parenthesis maka,

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell limit as x rightwards arrow thin space 0 minus of open parentheses open parentheses 3 x minus 1 close parentheses to the power of 5 close parentheses times limit as x rightwards arrow thin space 0 minus of open parentheses open parentheses 2 x plus 5 close parentheses squared close parentheses times limit as x rightwards arrow thin space 0 minus of open parentheses open parentheses 3 x to the power of 5 plus 6 x squared close parentheses to the power of negative 1 end exponent close parentheses end cell row blank equals cell open parentheses 3 times thin space 0 minus 1 close parentheses to the power of 5 times open parentheses 2 times thin space 0 plus 5 close parentheses squared times limit as x rightwards arrow thin space 0 minus of open parentheses fraction numerator 1 over denominator 3 x to the power of 5 plus 6 x squared end fraction close parentheses end cell row blank equals cell open parentheses 0 minus 1 close parentheses to the power of 5 times open parentheses 0 plus 5 close parentheses squared times fraction numerator 1 over denominator 3 open square brackets 0 close square brackets to the power of 5 plus 6 open square brackets 0 close square brackets squared end fraction end cell row blank equals cell open parentheses negative 1 close parentheses to the power of 5 times 5 squared times fraction numerator 1 over denominator 3 open square brackets 0 close square brackets plus 6 open square brackets 0 close square brackets end fraction end cell row blank equals cell negative 1 to the power of 5 times 25 times 1 over 0 end cell row blank equals cell negative 1 times 25 times infinity end cell row blank equals cell negative infinity end cell end table end style

 

Jadi, nilai . begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator open parentheses 3 x minus 1 close parentheses to the power of 5 open parentheses 2 x plus 5 close parentheses squared over denominator 3 x to the power of 5 plus 6 x squared end fraction end style  adalah negative infinity.

 

Jawaban terverifikasi

Dijawab oleh:

G. Albiah

Mahasiswa/Alumni Universitas Galuh Ciamis

Terakhir diupdate 11 Oktober 2021

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