Matematika Sekolah Menengah Atas Tolong Dibantu Donglim x->1 tan (x-1) sin(√x-1)/ x² - 2x+1 =​

esthermuellerulv – April 11, 2023

Tolong Dibantu Dong
lim x->1 tan (x-1) sin(√x-1)/ x² - 2x+1 =​

Penjelasan dengan langkah-langkah:

[tex] = \lim \limits_{x \to1} \frac{ \tan(x - 1) \sin( \sqrt{x} - 1) }{ {x}^{2} - 2x + 1 } [/tex]

[tex] = \lim \limits_{x \to1} \frac{ \tan(x - 1) \sin( \sqrt{x} - 1) }{(x - 1)(x - 1)} [/tex]

[tex] = \lim \limits_{x \to1} \frac{ \tan(x - 1) }{x - 1} \times \lim \limits_{x \to1} \frac{ \sin( \sqrt{x} - 1 ) }{x - 1} [/tex]

[tex] = \frac{1}{1} \times \lim \limits_{x \to1} \frac{ \sin( \sqrt{x} - 1 ) }{( \sqrt{x} + 1 )( \sqrt{x} - 1 )} [/tex]

[tex] = \lim \limits_{x \to1} \frac{ \sin( \sqrt{x} - 1 ) }{ \sqrt{x} - 1} \times \lim \limits_{x \to1} \frac{1}{ \sqrt{x} + 1 } [/tex]

[tex] = \frac{1}{1} \times \frac{1}{ \sqrt{1} + 1} [/tex]

[tex] = \frac{1}{1 + 1} [/tex]

[tex] = \frac{1}{2} [/tex]

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