Question

求limx趋近于0tanx-sinx/x三次方

Answer 1

(tanx-sinx)/x^3
=(sinx(1-cosx)/cosx)/x^3
=2sinx*sin^2 (x/2) /(x^3 * cosx)
注意到lim sinx / x = lim sin(x/2) / (x/2) = 1
lim cosx = 1
有原式 = lim (sinx / x)*[sin(x/2) / (x/2)]^2 /2cosx
=1/2

Answer 2

(tanx-sinx)/x^3=sinx*(1-cosx)/x^3=(1-cosx)/x^2=1/2,x趋近于0时

Answer 3

lim(x->0)(tanx-sinx)/x^3 (0/0)
=lim(x->0)( (secx)^2 - cosx) /(3x^2) (0/0)
=lim(x->0) ( 2(secx)^2tanx +sinx ) / (6x) (0/0)
= lim(x->0) ( 2[ (secx)^4 + 2(secx)^2(tanx)^2] + cosx ) /6
= 1/2

Answer 4

lim(x→0) (tanx-sinx)/x^3

=lim(x→0) tanx(1-cosx)/x^3
=lim(x→0) x*(x^2/2)/x^3
=1/2

Answer 5

lim （x→0） (sinx-tanx)/x^3
=lim （x→0） tanx(cosx-1)/x^3
=lim （x→0） x(-1/2x^2)/x^3
=-1/2