Tolong bantu, jangan ngasal!.... Question from @AmiFadhilaa

ekamiaww $1)~ \lim_{x \to -3} \frac{x^2+6x+9}{2-2cos(2x+6)} ~~selesaikan\ dgn\ dalil\ L'Hospital\ (turunan)\\ ~=\lim_{x \to -3} \frac{2x+6}{-2.-2sin(2x+6)} \\ ~=\lim_{x \to -3} \frac{2x+6}{4sin(2x+6)} \\ ~= \frac{1}{4}\times \frac{2}{2} \\ ~= \frac{1}{4}$

$2)~ \lim_{x \to 1} \frac{tan(x-1).sin(1- \sqrt{x} )}{x^2-2x+1} \\ ~= \lim_{x \to 1} \frac{tan(x-1).sin(1- \sqrt{x} )}{(x-1)(x-1)} \\ ~= \lim_{x \to 1} \frac{tan(x-1).sin(1- \sqrt{x} )}{(x-1)(( \sqrt{x} -1)( \sqrt{x} +1))} \\ ~= \lim_{x \to 1} \frac{tan(x-1).sin(1- \sqrt{x} )}{(x-1)(-(1-\sqrt{x} )( \sqrt{x} +1))} \\ ~= \lim_{x \to 1} \frac{tan(x-1).sin(1- \sqrt{x} )}{(x-1)(-(1-\sqrt{x} )( \sqrt{x} +1))}$
$~= \lim_{x \to 1} \frac{tan(x-1)}{(x-1)} \times \frac{sin(1- \sqrt{x} )}{-(1-\sqrt{x} )} \times \frac{1}{ \sqrt{x} +1} \\ ~=1\times -1\times \frac{1}{ \sqrt{1} +1} \\ ~=-\frac{1}{ 2}$

$3)~\lim_{x \to \pi } \frac{sin(x- \pi )}{2(x- \pi )+tan(x- \pi )} ~~~gunakan\ L'Hospital \\ ~=\lim_{x \to \pi } \frac{cos(x- \pi )}{2+sec^2(x- \pi )} \\ ~=\frac{cos( \pi - \pi )}{2+sec^2( \pi - \pi )} \\ ~= \frac{cos\ 0}{2+sec^2\ 0} \\ ~= \frac{1}{2+1^2} \\ ~= \frac{1}{3}$

semoga membantu :) maaf tidak bisa bantu semuanya :)

1 votes Thanks 1

AmiFadhilaa makasi banyak mba eka :D

ekamiaww sama2 ami :*

MathSolver74 Ngelanjutin punya eka

5) lim (2 sin² x/2)/x sin x = 2(x²/4)/x² = 1/2
x-> 0

6) lim (1 - (1 - 2sin² 4x))/(sin 2x tan 2x)
x-> 0
= lim (2sin² 4x)/(sin 2x tan 2x)
x-> 0
= 2(16x²)/4x²
= 8

1 votes Thanks 2

AmiFadhilaa makasi banyak kak insan :D

MathSolver74 masama ami :*

Larutan asam HA 0,1 M akan memberikan warna yang sama dengan larutan HCL 0,01 M jika ditetesi dengan indikator universal. hitunglah nilai Ka HA!

Bantu nomer 4 sama 5 dong, JANGAN NGASAL

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