Pertanyaan

N i l ai d a r i x → ∞ lim ( 4 x 2 − 2 x − 5 − ( 2 x − 2 ) 2 ) = ....

$N i l ai d a r i x \to \infty lim (4 x^{2} - 2 x - 5 - (2 x - 2)^{2}) = ....$

-2

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

$M e n e n t u k a n space n i l a i limit as x rightwards arrow infinity of open square brackets square root of a x squared plus b x plus c end root minus square root of p x squared plus q r plus r end root close square brackets J i k a space a equals p comma space m a k a limit as x rightwards arrow infinity of open square brackets square root of a x squared plus b x plus c end root minus square root of p x squared plus q r plus r end root close square brackets equals fraction numerator b minus q over denominator 2 square root of a end fraction J i k a space a not equal to p comma space m a k a limit as x rightwards arrow infinity of open square brackets square root of a x squared plus b x plus c end root minus square root of p x squared plus q r plus r end root close square brackets equals plus-or-minus tilde J a d i... limit as x rightwards arrow infinity of open square brackets square root of 4 x squared minus 2 x minus 5 end root minus square root of left parenthesis 2 x minus 2 right parenthesis squared end root close square brackets equals limit as x rightwards arrow infinity of open square brackets square root of 4 x squared minus 2 x minus 5 end root minus square root of 4 x squared minus 8 x plus 4 end root close square brackets rightwards double arrow a equals p equals 4 K a r e n a space a equals p space m a k a space b e r l a k u space r u m u s limit as x rightwards arrow infinity of open square brackets square root of a x squared plus b x plus c end root minus square root of p x squared plus q r plus r end root close square brackets equals fraction numerator b minus q over denominator 2 square root of a end fraction equals limit as x rightwards arrow infinity of open square brackets square root of 4 x squared minus 2 x minus 5 end root minus square root of 4 x squared minus 8 x plus 4 end root close square brackets equals fraction numerator negative 2 minus left parenthesis negative 8 right parenthesis over denominator 2 square root of 4 end fraction equals fraction numerator 6 over denominator 2.2 end fraction equals 6 over 4 equals 3 over 2$