Question

lim(x→0+)[ln(sin5x)]/[ln(sin3x)] 这题咋做

Answer 1

lim(x→0+)[ln(sin5x)]/[ln(sin3x)]

=lim(x→0+)[5cos5x/sin5x]/[3cos3x/sin3x]

=lim(x→0+)[5cos5x×sin3x]/[3cos3x×sin5x]

=1（L'Hospital法则）

补充：lim(x→0+)cos5x=1,lim(x→0+)cos3x=1,因为这是连续函数求极限,直接代入.

lim(x→0+)[sin3x/sin5x]

=3/5