شاه کلید نکات
شاه کلید سوال
با استفاده از نمودار f(x) = sinx و g(x) = cosx حدهای زیر را بیابید.
الف \(\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \;\sin x\)
ب \(\mathop {\lim }\limits_{x \to - \pi } \;\sin x\)
پ \(\mathop {\lim }\limits_{x \to {{\frac{\pi }{3}}^ - }} \;\sin x\)
ت \(\mathop {\lim }\limits_{x \to {\pi ^ + }} \;\sin x\)
ث \(\mathop {\lim }\limits_{x \to 0} \;\cos x\)
ج \(\mathop {\lim }\limits_{x \to {{\frac{\pi }{4}}^ - }} \;\sin x\)
چ \(\mathop {\lim }\limits_{x \to \frac{{ - \pi }}{2}} \;\cos x\)
ح \(\mathop {\lim }\limits_{x \to {{\frac{\pi }{3}}^ + }} \;\cos x\)
الف \(\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \;\sin x = \sin \frac{\pi }{2} = 1\)
ب \(\mathop {\lim }\limits_{x \to - \pi } \;\sin x = \sin ( - \pi ) = - \sin \pi = 0\)
پ \(\mathop {\lim }\limits_{x \to {{\frac{\pi }{3}}^ - }} \;\sin x = \sin \frac{{{\pi ^ - }}}{3} = \frac{{\sqrt 3 }}{2}\)
ت \(\mathop {\lim }\limits_{x \to {\pi ^ + }} \;\sin x = \sin {\pi ^ + } = 0\)
ث \(\mathop {\lim }\limits_{x \to 0} \;\cos x = \cos \:0 = 1\)
ج \(\mathop {\lim }\limits_{x \to {{\frac{\pi }{4}}^ - }} \;\sin x = \cos \:(\frac{{{\pi ^ - }}}{4}) = \frac{{\sqrt 2 }}{2}\)
چ \(\mathop {\lim }\limits_{x \to \frac{{ - \pi }}{2}} \;\cos x = \cos (\frac{{ - \pi }}{2}) = 0\)
ح \(\mathop {\lim }\limits_{x \to {{\frac{\pi }{3}}^ + }} \;\cos x = \cos \:(\frac{{{\pi ^ + }}}{3}) = \frac{1}{2}\)
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