第8题怎么做,需要详细过程,谢谢。
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lim(x→0) [3+f(x)]/x^4
=lim(x→0) [3x²+x²f(x)+sin3x²-sin3x²]/x^6
=lim(x→0) [x²f(x)+sin3x²]/x^6 + lim(x→0) [3x²-sin3x²]/x^6
=lim(x→0) [3x²-sin3x²]/x^6 (0/0型 用洛必达)
=lim(x→0) (6x-6xcos3x²)/(6x^5)
=lim(x→0) (1-cos3x²)/x^4
=lim(x→0) [(3x²)²/2]/x^4
=9/2
=lim(x→0) [3x²+x²f(x)+sin3x²-sin3x²]/x^6
=lim(x→0) [x²f(x)+sin3x²]/x^6 + lim(x→0) [3x²-sin3x²]/x^6
=lim(x→0) [3x²-sin3x²]/x^6 (0/0型 用洛必达)
=lim(x→0) (6x-6xcos3x²)/(6x^5)
=lim(x→0) (1-cos3x²)/x^4
=lim(x→0) [(3x²)²/2]/x^4
=9/2
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