Roboguru

Nilai dari  adalah ...

Pertanyaan

Nilai dari limit as x rightwards arrow negative 3 of open parentheses fraction numerator x squared plus 3 x over denominator square root of 2 x plus 15 end root minus 3 end fraction close parentheses adalah ...

Pembahasan Soal:

Diketahui limit pecahan bentuk akar. Untuk menyelesaikan permasalahan pada soal kita dapat mengkalikannya dengan bentuk sekawan seperti berikut:

equals limit as x rightwards arrow negative 3 of fraction numerator x squared plus 3 x over denominator square root of 2 x plus 15 end root minus 3 end fraction cross times fraction numerator square root of 2 x plus 15 end root plus 3 over denominator square root of 2 x plus 15 end root plus 3 end fraction equals limit as x rightwards arrow negative 3 of fraction numerator open parentheses x squared plus 3 x close parentheses open parentheses square root of 2 x plus 15 end root plus 3 close parentheses over denominator left parenthesis 2 x plus 15 right parenthesis minus 9 end fraction equals limit as x rightwards arrow negative 3 of fraction numerator x left parenthesis x plus 3 right parenthesis open parentheses square root of 2 x plus 15 end root plus 3 close parentheses over denominator 2 x plus 15 minus 9 end fraction equals limit as x rightwards arrow negative 3 of fraction numerator x left parenthesis x plus 3 right parenthesis open parentheses square root of 2 x plus 15 end root plus 3 close parentheses over denominator 2 x plus 6 end fraction equals limit as x rightwards arrow negative 3 of fraction numerator x up diagonal strike left parenthesis x plus 3 right parenthesis end strike open parentheses square root of 2 x plus 15 end root plus 3 close parentheses over denominator 2 up diagonal strike left parenthesis x plus 3 right parenthesis end strike end fraction equals fraction numerator negative 3 open parentheses square root of 2 left parenthesis negative 3 right parenthesis plus 15 end root plus 3 close parentheses over denominator 2 end fraction equals fraction numerator negative 3 left parenthesis square root of 9 plus 3 right parenthesis over denominator 2 end fraction equals fraction numerator negative 3 left parenthesis 3 plus 3 right parenthesis over denominator 2 end fraction equals fraction numerator negative 3 cross times 6 over denominator 2 end fraction equals fraction numerator negative 18 over denominator 2 end fraction equals negative 9

Jadi, hasil dari limit as x rightwards arrow negative 3 of fraction numerator x squared plus 3 x over denominator square root of 2 x plus 15 end root minus 3 end fraction adalah negative 9  

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Juni 2021

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