Question

limx→0,[{(sinx)^2,0}ln(1+t)dt]/x^4

Answer 1

∵ln(1+(sinx)^2~（sinx)^2

∴limx→0,[{(sinx)^2,0}ln(1+t)dt]/x^4=lim(x→0)[ln(1+(sinx)^2]2sinxcosx)/4x^3

=lim(x→0)2(sinx)^3/4x^3=1/2