Pertanyaan

N i l ai d a r i x → 2 lim ( 3 − x 2 + 5 ) x − 2 = ....

$N i l ai d a r i x \to 2 lim \frac{x - 2}{( 3 - x ^{2} + 5 )} = ....$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

$limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator open parentheses 3 minus square root of x squared plus 5 end root close parentheses end fraction equals limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator open parentheses 3 minus square root of x squared plus 5 end root close parentheses end fraction cross times fraction numerator 3 plus square root of x squared plus 5 end root over denominator 3 plus square root of x squared plus 5 end root end fraction equals limit as x rightwards arrow 2 of fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis over denominator left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis end fraction equals limit as x rightwards arrow 2 of fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis over denominator 9 minus left parenthesis x squared plus 5 right parenthesis end fraction equals limit as x rightwards arrow 2 of fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis over denominator negative x squared plus 4 end fraction equals limit as x rightwards arrow 2 of fraction numerator left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis over denominator negative left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis end fraction equals limit as x rightwards arrow 2 of fraction numerator left parenthesis 3 plus square root of x squared plus 5 end root right parenthesis over denominator negative left parenthesis x plus 2 right parenthesis end fraction equals fraction numerator open parentheses 3 plus square root of 2 squared plus 5 end root close parentheses over denominator negative left parenthesis 2 plus 2 right parenthesis end fraction equals negative 3 over 2$