lim(x→0) (5x+sin^2 x -2x^3)/(tanx+4x^2) 用等价无穷小怎么算

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 06:41:14
lim(x→0) (5x+sin^2 x -2x^3)/(tanx+4x^2) 用等价无穷小怎么算

lim(x→0) (5x+sin^2 x -2x^3)/(tanx+4x^2) 用等价无穷小怎么算
lim(x→0) (5x+sin^2 x -2x^3)/(tanx+4x^2) 用等价无穷小怎么算

lim(x→0) (5x+sin^2 x -2x^3)/(tanx+4x^2) 用等价无穷小怎么算
当x→0时,x近似=sinx近似=tanx,
这样lim(x→0) (5x+sin^2 x -2x^3)/(tanx+4x^2)
 =lim(x→0) (5x+x^2 -2x^3)/(x+4x^2)
=lim(x→0) (5+ x -2x^2)/(1+4x)
=5

洛必达法则

楼上做法错误了,涉及加减关系时,不能用等价无穷小
lim(x→0) (5x + sin²x - 2x³)/(tanx + 4x²)、0/0不定型,运用洛必达法则
= lim(x→0) (5 + sin2x - 6x²)/(sec²x + 8x)
= (5 + 0 - 0)/(1 + 0)
= 5