Hasil dari lim x ---> 0[tex] \frac{1 - \sqrt{ cos\: x } }{ {x}^{2} } [/tex].... Question from @manusia162

September 2022 1 7 Report

Hasil dari lim x ---> 0
[tex] \frac{1 - \sqrt{ cos\: x } }{ {x}^{2} } [/tex]

Hasil dari $\displaystyle{ \lim_{x \to 0} \frac{1-\sqrt{cosx}}{x^2}}$ adalah $\displaystyle{\boldsymbol{\frac{1}{4}} }$ .

PEMBAHASAN

Teorema pada limit adalah sebagai berikut :

$(i)~\lim\limits_{x \to c} f(x)=f(c)$

$(ii)~\lim\limits_{x \to c} kf(x)=k\lim\limits_{x \to c} f(x)$

$(iii)~\lim\limits_{x \to c} [f(x)\pm g(x)]=\lim\limits_{x \to c} f(x)\pm\lim\limits_{x \to c} g(x)$

$(iv)~\lim\limits_{x \to c} [f(x)\times g(x)]=\lim\limits_{x \to c} f(x)\times\lim\limits_{x \to c} g(x)$

$\displaystyle{(v)~\lim\limits_{x \to c} \left [ \frac{f(x)}{g(x)} \right ]=\frac{\lim\limits_{x \to c} f(x)}{\lim\limits_{x \to c} g(x)} }$

$(vi)~\lim\limits_{x \to c} \left [ f(x) \right ]^n=\left [ \lim\limits_{x \to c} f(x) \right ]^n$

Rumus untuk limit fungsi trigonometri :

$\displaystyle{(i)~\lim\limits_{x \to 0} \frac{sinax}{bx}=\lim\limits_{x \to 0} \frac{tanax}{bx}=\frac{a}{b} }$

$\displaystyle{(ii)~\lim\limits_{x \to 0} \frac{ax}{sinbx}=\lim\limits_{x \to 0} \frac{ax}{tanbx}=\frac{a}{b} }$

$\displaystyle{(iii)~\lim\limits_{x \to 0} \frac{sinax}{sinbx}=\lim\limits_{x \to 0} \frac{tanax}{tanbx}=\frac{a}{b} }$

$\displaystyle{(iv)~\lim\limits_{x \to a} \frac{sin(x-a)}{(x-a)}=\lim\limits_{x \to a} \frac{tan(x-a)}{(x-a)}=1 }$

DIKETAHUI

$\displaystyle{ \lim_{x \to 0} \frac{1-\sqrt{cosx}}{x^2}= }$

DITANYA

Tentukan hasilnya.

PENYELESAIAN

$\displaystyle{ \lim_{x \to 0} \frac{1-\sqrt{cosx}}{x^2}}$

$\displaystyle{=\lim_{x \to 0} \frac{1-\sqrt{cosx}}{x^2}\times\frac{1+\sqrt{cosx}}{1+\sqrt{cosx}}}$

$\displaystyle{=\lim_{x \to 0} \frac{1-cosx}{x^2(1+\sqrt{cosx})}\times\frac{1+cosx}{1+cosx} }$

$\displaystyle{=\lim_{x \to 0} \frac{1-cos^2x}{x^2(1+\sqrt{cosx})(1+cosx)} }$

$\displaystyle{=\lim_{x \to 0} \frac{sin^2x}{x^2(1+\sqrt{cosx})(1+cosx)} }$

$\displaystyle{=\lim_{x \to 0} \frac{sin^2x}{x^2}\times\lim_{x \to 0} \frac{1}{1+\sqrt{cosx}}\times\lim_{x \to 0} \frac{1}{1+cosx} }$

$\displaystyle{=\lim_{x \to 0} \left ( \frac{sinx}{x} \right )^2\times\frac{1}{1+\sqrt{cos0}}\times \frac{1}{1+cos0} }$

$\displaystyle{=\left ( \lim_{x \to 0} \frac{sinx}{x} \right )^2\times\frac{1}{1+\sqrt{1}}\times \frac{1}{1+1} }$

$\displaystyle{=\left ( 1 \right )^2\times\frac{1}{2}\times \frac{1}{2} }$

$\displaystyle{=\frac{1}{4} }$

KESIMPULAN

Hasil dari $\displaystyle{ \lim_{x \to 0} \frac{1-\sqrt{cosx}}{x^2}}$ adalah $\displaystyle{\boldsymbol{\frac{1}{4}} }$ .

PELAJARI LEBIH LANJUT

Limit fungsi trigonometri : brainly.co.id/tugas/41998117
Limit trigonometri : brainly.co.id/tugas/38915095
Limit trigonometri : brainly.co.id/tugas/30308496

DETAIL JAWABAN

Kelas : 11

Mapel: Matematika

Bab : Limit Fungsi

Kode Kategorisasi: 11.2.8

3 votes Thanks 1

PEMBAHASAN

DIKETAHUI

DITANYA

PENYELESAIAN

KESIMPULAN

PELAJARI LEBIH LANJUT

DETAIL JAWABAN

Apa Verb 1,2, dan 3 dari drink?

Pensil yang memiliki banyak karbon adalah... A. 3H B. 3B C. 4H D. 4B E. 5H

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