Pertanyaan

Hitunglah nilai limit fungsi berikut: x → 1 lim ( x − 1 ) 2 ( 2 x − 3 x + 1 ) ( x − 1 )

Hitunglah nilai limit fungsi berikut:

$x \to 1 lim \frac{( 2 x - 3 x + 1 ) ( x - 1 )}{( x - 1 ) ^{2}}$

B. Hary

Master Teacher

Jawaban terverifikasi

Pembahasan

$limit as x rightwards arrow 1 of fraction numerator left parenthesis 2 x minus 3 square root of x plus 1 right parenthesis left parenthesis square root of x minus 1 right parenthesis over denominator open parentheses x minus 1 close parentheses squared end fraction left right double arrow limit as x rightwards arrow 1 of fraction numerator left parenthesis 2 x minus 3 square root of x plus 1 right parenthesis left parenthesis square root of x minus 1 right parenthesis over denominator open parentheses x minus 1 close parentheses open parentheses x minus 1 close parentheses end fraction times fraction numerator square root of x plus 1 over denominator square root of x plus 1 end fraction left right double arrow limit as x rightwards arrow 1 of fraction numerator open parentheses 2 square root of x minus 1 close parentheses open parentheses square root of x minus 1 close parentheses left parenthesis x minus 1 right parenthesis over denominator left parenthesis x minus 1 right parenthesis open parentheses x minus 1 close parentheses open parentheses square root of x plus 1 close parentheses end fraction left right double arrow limit as x rightwards arrow 1 of fraction numerator left parenthesis 2 square root of x minus 1 right parenthesis left parenthesis square root of x minus 1 right parenthesis over denominator open parentheses x minus 1 close parentheses open parentheses square root of x plus 1 close parentheses end fraction left right double arrow limit as x rightwards arrow 1 of fraction numerator left parenthesis 2 square root of x minus 1 right parenthesis left parenthesis square root of x minus 1 right parenthesis over denominator open parentheses square root of x minus 1 close parentheses open parentheses square root of x plus 1 close parentheses open parentheses square root of x plus 1 close parentheses end fraction left right double arrow limit as x rightwards arrow 1 of fraction numerator left parenthesis 2 square root of x minus 1 right parenthesis over denominator open parentheses square root of x plus 1 close parentheses open parentheses square root of x plus 1 close parentheses end fraction equals 1 fourth$