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lim x→0 tan x/x=
lim(x→0)tan(x)^2/sin3x
Limit, thank you
General solution:
lim(x→0) tan²x/sin3x
=lim(x→0) sin²x/cos²x*1/sin3x
=lim(x→0) sin²x/x²*x²/cos²x*3x/sin3x*1/3x
=lim(x→0) (sinx/x)²*(3x/sin3x)*(x/3)
=1²*1*0/3
=0
[x approaches 0] Lim X / ln (1 + x) = 1, right
lim(1/ln(1+x)-1/x)
=lim[x-ln(1+x)]/xln(1+x)
=lim[1-1/(1-x)]/[ln(1+x)+x/(1+x)]
=limx/[x+(1+x)ln(1+x)]
=lim1/[ln(1+x)+1+1]=1/2
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