Pertanyaan

Nilai dari x → 2 lim x − 2 3 − x + 7 adalah ....

Nilai dari $x \to 2 lim \frac{3 - x + 7}{x - 2}$ adalah ....

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

nilai x → 2 lim x − 2 3 − x + 7 = − 3 1

nilai

x \to 2 lim \frac{3 - x + 7}{x - 2} = - \frac{1}{3}

Pembahasan

Jadi nilai x → 2 lim x − 2 3 − x + 7 = − 3 1

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator 3 minus square root of x plus 7 end root over denominator x minus 2 end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator 3 minus square root of x plus 7 end root over denominator x minus 2 end fraction cross times fraction numerator 3 plus square root of x plus 7 end root over denominator 3 plus square root of x plus 7 end root end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 3 squared minus left parenthesis x plus 7 right parenthesis over denominator left parenthesis x minus 2 right parenthesis cross times open parentheses square root of x plus 7 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator negative x plus 2 over denominator left parenthesis x minus 2 right parenthesis cross times open parentheses square root of x plus 7 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator negative 1 over denominator square root of x plus 7 end root end fraction end cell row blank equals cell fraction numerator negative 1 over denominator square root of 2 plus 7 end root end fraction end cell row blank equals cell negative 1 third end cell end table end style$

Jadi nilai $x \to 2 lim \frac{3 - x + 7}{x - 2} = - \frac{1}{3}$