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Tuesday, 21 August 2018
Pembahasan Limit Trigonometri Tanpa Turunan
SOAL :
SEMOGA BERMANFAAT
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&space;%5C%5C&space;%5C%5CJawab&space;:&space;%5C%5C&space;%5C%5Clim_%7Ba%5Crightarrow&space;0&space;%7D%5Cfrac%7B1%7D%7Ba%7D%5Cleft&space;(&space;%5Cfrac%7Bsin%5E%7B3%7Da+sin2a%5C,&space;cos%5E%7B2%7D2a%7D%7Bcos2a%7D%5Cright&space;)&space;%5C%5C&space;%5C%5Clim_%7Ba%5Crightarrow&space;0&space;%7D%5Cfrac%7B1%7D%7Ba%7D%5Cleft&space;(&space;%5Cfrac%7Bsin%5E%7B3%7Da+2sina%5C,&space;cosa%5C,%5Cleft&space;(1-sin%5E%7B2%7D2a&space;%5Cright&space;)&space;%7D%7Bcos2a%7D%5Cright&space;)&space;%5C%5C&space;%5C%5Clim_%7Ba%5Crightarrow&space;0&space;%7D%5Cfrac%7B1%7D%7Ba%7D%5Cleft&space;(&space;%5Cfrac%7Bsin%5E%7B3%7Da+2sina%5C,&space;cosa%5C,-2sina&space;%5C,&space;cosa&space;%5C,&space;sin%5E%7B2%7D2a)&space;%7D%7Bcos2a%7D%5Cright&space;)&space;%5C%5C&space;%5C%5Clim_%7Ba%5Crightarrow&space;0&space;%7D%5Cfrac%7Bsina%7D%7Ba%7D%5Cleft&space;(&space;%5Cfrac%7Bsin%5E%7B2%7Da+2%5C,&space;cosa%5C,-2&space;%5C,&space;cosa&space;%5C,&space;sin%5E%7B2%7D2a)&space;%7D%7Bcos2a%7D%5Cright&space;)&space;%5C%5C&space;%5C%5C(1)%5Cleft&space;(&space;%5Cfrac%7Bsin%5E%7B2%7D0+2%5C,&space;cos0%5C,-2&space;%5C,&space;cos0&space;%5C,&space;sin%5E%7B2%7D0)&space;%7D%7Bcos0%7D%5Cright&space;)&space;%5C%5C&space;%5C%5C(1)%5Cleft&space;(&space;%5Cfrac%7B0+2.1%5C,-2.1.0)&space;%7D%7B1%7D%5Cright&space;)=2 "\\\lim_{a\rightarrow 0 }\frac{1}{a}\left ( \frac{sin^{3}a}{cos2a}+sin2a\, cos2a\,\right ) \\ \\Jawab : \\ \\lim_{a\rightarrow 0 }\frac{1}{a}\left ( \frac{sin^{3}a+sin2a\, cos^{2}2a}{cos2a}\right ) \\ \\lim_{a\rightarrow 0 }\frac{1}{a}\left ( \frac{sin^{3}a+2sina\, cosa\,\left (1-sin^{2}2a \right ) }{cos2a}\right ) \\ \\lim_{a\rightarrow 0 }\frac{1}{a}\left ( \frac{sin^{3}a+2sina\, cosa\,-2sina \, cosa \, sin^{2}2a) }{cos2a}\right ) \\ \\lim_{a\rightarrow 0 }\frac{sina}{a}\left ( \frac{sin^{2}a+2\, cosa\,-2 \, cosa \, sin^{2}2a) }{cos2a}\right ) \\ \\(1)\left ( \frac{sin^{2}0+2\, cos0\,-2 \, cos0 \, sin^{2}0) }{cos0}\right ) \\ \\(1)\left ( \frac{0+2.1\,-2.1.0) }{1}\right )=2")
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