Pertanyaan

Tentukan nilai dari x → − 2 lim x + 2 2 x + 13 − x + 11 .

Tentukan nilai dari $x \to - 2 lim \frac{2 x + 13 - x + 11}{x + 2}$ .

J. Joko

Master Teacher

Jawaban terverifikasi

Jawaban

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, $begin mathsize 14px style limit as x rightwards arrow negative 2 of fraction numerator square root of 2 x plus 13 end root minus square root of x plus 11 end root over denominator x plus 2 end fraction equals 1 over 6 end style$

Pembahasan

Substitusi Karena bentuk tak tentu, maka dikali akar sekawan dahulu Jadi ,

Substitusi

Karena bentuk tak tentu, maka dikali akar sekawan dahulu

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow negative 2 of fraction numerator square root of 2 x plus 13 end root minus square root of x plus 11 end root over denominator x plus 2 end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of open parentheses fraction numerator square root of 2 x plus 13 end root minus square root of x plus 11 end root over denominator x plus 2 end fraction times fraction numerator square root of 2 x plus 13 end root plus square root of x plus 11 end root over denominator square root of 2 x plus 13 end root plus square root of x plus 11 end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator 2 x plus 13 minus left parenthesis x plus 11 right parenthesis over denominator left parenthesis x plus 2 right parenthesis left parenthesis square root of 2 x plus 13 end root plus square root of x plus 11 end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator 2 x plus 13 minus x minus 11 over denominator left parenthesis x plus 2 right parenthesis left parenthesis square root of 2 x plus 13 end root plus square root of x plus 11 end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator x plus 2 over denominator left parenthesis x plus 2 right parenthesis left parenthesis square root of 2 x plus 13 end root plus square root of x plus 11 end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator 1 over denominator square root of 2 x plus 13 end root plus square root of x plus 11 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 2 times left parenthesis negative 2 right parenthesis plus 13 end root plus square root of negative 2 plus 11 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 9 plus square root of 9 end fraction end cell row blank equals cell fraction numerator 1 over denominator 3 plus 3 end fraction end cell row blank equals cell 1 over 6 end cell row blank blank blank end table end style$

Jadi, $begin mathsize 14px style limit as x rightwards arrow negative 2 of fraction numerator square root of 2 x plus 13 end root minus square root of x plus 11 end root over denominator x plus 2 end fraction equals 1 over 6 end style$