求极值lim(x→0)(cos5x-cos3x)/x²lim(x→0)(cos5x-cos3x)/x²
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求极值lim(x→0)(cos5x-cos3x)/x²lim(x→0)(cos5x-cos3x)/x²求极值lim(x→0)(cos5x-cos3x)/x²lim(x→0
求极值lim(x→0)(cos5x-cos3x)/x²lim(x→0)(cos5x-cos3x)/x²
求极值lim(x→0)(cos5x-cos3x)/x²
lim(x→0)(cos5x-cos3x)/x²
求极值lim(x→0)(cos5x-cos3x)/x²lim(x→0)(cos5x-cos3x)/x²
显然x趋于0的时候,分子cos5x-cos3x和分母x²都趋于0
满足洛必达法则使用的条件,
那么
原极限
=lim(x→0)(cos5x-cos3x)' / (x²)'
=lim(x→0) (-5sin5x +3sin3x) /2x
显然
lim(x→0) sin5x /2x=5/2,lim(x→0) sin3x /2x=3/2
所以
原极限
= -5 *5/2 +3*3/2
= -8
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