[tex] \lim_{x \to \ \pi /4 sin²x - cos²x / sin x - cos x =
Matematika
Alfikaauliana
Pertanyaan
[tex] \lim_{x \to \ \pi /4 sin²x - cos²x / sin x - cos x =
2 Jawaban
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1. Jawaban Gallz22
=Lim (sin²x - cos²x) / sin x - cos x
=Lim
(sin x + cos x)(sin x - cos x)/sin x - cosx
=lim (sin x + cos x)
=sin 45 + cos 45
=√2 -
2. Jawaban whongaliem
[tex] \lim_{x \to \ \frac{ \pi }{4} } \frac{ sin^{2} x - cos^{2} x}{sin x - cos x} = \lim_{x \to \ \frac{ \pi }{4} } \frac{(sin x + cos x)(sin x - cos x)}{sin x - cos x} [/tex]
[tex]= \lim_{x \to \ \frac{ \pi }{4} } sin x + cos x[/tex]
[tex]= sin \frac{ \pi }{4} + cos \frac{ \pi }{4} [/tex]
[tex]= \frac{1}{2} \sqrt{2} + \frac{1}{2} \sqrt{2} [/tex]
= √2