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Tentukan nilai dari soal di bawah ini 1.

Pertanyaan

Tentukan nilai dari soal di bawah ini
1. begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x cubed plus 4 x squared minus 12 x over denominator x to the power of 6 minus 5 x to the power of 4 plus 6 x squared end fraction end style 

  1. ...begin mathsize 14px style space end style 

  2. ...begin mathsize 14px style space end style 

Pembahasan Soal:

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x cubed plus 4 x squared minus 12 x over denominator x to the power of 6 minus 5 x to the power of 4 plus 6 x squared end fraction end style jika substitusi nilai begin mathsize 14px style x equals 0 end style akan menghasilkan begin mathsize 14px style 0 over 0 end style, sehingga bentuk limit perlu diubah
begin mathsize 14px style table row blank cell limit as x rightwards arrow 0 of fraction numerator x cubed plus 4 x squared minus 12 x over denominator x to the power of 6 minus 5 x to the power of 4 plus 6 x squared end fraction end cell row equals cell limit as x rightwards arrow 0 of fraction numerator up diagonal strike x open parentheses x squared plus 4 x minus 12 close parentheses over denominator up diagonal strike x open parentheses x to the power of 5 minus 5 x cubed plus 6 x squared close parentheses end fraction end cell row equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses x squared plus 4 x minus 12 close parentheses over denominator open parentheses x to the power of 5 minus 5 x cubed plus 6 x squared close parentheses end fraction end cell end table end style

substitusikan kembali nilai begin mathsize 14px style x equals 0 end style maka diperoleh begin mathsize 14px style 12 over 0 equals infinity end style

jadi nilai size 14px lim with size 14px x size 14px rightwards arrow size 14px 0 below fraction numerator size 14px x to the power of size 14px 3 size 14px plus size 14px 4 size 14px x to the power of size 14px 2 size 14px minus size 14px 12 size 14px x over denominator size 14px x to the power of size 14px 6 size 14px minus size 14px 5 size 14px x to the power of size 14px 4 size 14px plus size 14px 6 size 14px x to the power of size 14px 2 end fraction equals infinity 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 11 Februari 2021

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