📋 Daftar Isi
Contoh 1
\[
\lim_{x\rightarrow \frac{\pi}{4}}\frac{cos x-sin x}{cos 2x}
\]
\[
=\lim_{x\rightarrow \frac{\pi}{4}}\frac{cos x-sin x}{cos^{2}x-sin^{2}x}
\]
\[
\lim_{x\rightarrow \frac{\pi}{4}}\frac{cos x-sin x}{(cos x – sin x)(cos x+ sin x)}
\]
\[
\lim_{x\rightarrow \frac{\pi}{4}}\frac{1}{(cos x + sin x)}
\]
\[
=\frac{1}{2}\sqrt{2}
\]
Contoh 2
\[
\lim_{x\rightarrow 0}\frac{3.sin4x}{5.tan6x}
\]
\[
=\frac{3.4x}{5.6x}
\]
\[
=\frac{2}{5}
\]
Contoh 3
\[
\lim_{x\rightarrow 0}\frac{1-cos4x}{x.tan3x}
\]
\[
=\lim_{x\rightarrow 0}\frac{1-(1-2sin^{2}2x}{x.tan3x}
\]
\[
=\lim_{x\rightarrow 0}\frac{2sin^{2}2x}{x.tan3x}
\]
\[
\frac{2(2x)^{2}}{x.3x}
\]
\[
=\frac{8}{3}
\]
Contoh 4
\[
lim_{x\rightarrow a}\frac{(2a+x)sin(a-x)}{x^{2}-a^{2}}
\]
\[
=lim_{x\rightarrow a}\frac{(2a+x)sin(a-x)}{-(x+a)(x+a)}
\]
\[
=\frac{(2a+a)}{-(a+a)}
\]
\[
=-\frac{3}{2}
\]
Contoh 5
\[
\lim_{x\rightarrow 3}\frac{x^{4}-9x^{2}}{sin(9-x^{2})}
\]
\[
=\lim_{x\rightarrow 3}\frac{-x^{2}(-x^{2}+9)}{sin(9-x^{2})}
\]
\[
=-(3)^{2}
\]
\[
=-9
\]
Contoh 6
\[
\lim_{x\rightarrow \frac{\pi}{2}}\frac{1+cos2x}{cosx}
\]
\[
=\lim_{x\rightarrow \frac{\pi}{2}}\frac{1+2cos^{2}x-1}{cosx}
\]
\[
=\lim_{x\rightarrow \frac{\pi}{2}}2cosx
\]
\[
=0
\]
Materi Lengkap
Berikut adalah beberapa materi lengkap yang membahas tuntas mengenai Limit.
