Limit[(Cos[4 x]^(1/4)-Cos[2 x Exp[x^2]])/(Sin[2 x] -2Tan[x])^2,x-> 0]

Неопределенность вида 0/0

Limit[(x+ 2^x)^(1/x),x-> ∞]

Limit[(3^(x^3)+x^2)/3^(x^3+x),x-> ∞]

Limit[x^3 (Sqrt[x^2 +Sqrt[x^4+1]]-x Sqrt[2]),x-> ∞]

Limit[x^3 (Sqrt[x^2 +Sqrt[x^4+1]]-x Sqrt[2]),x-> -∞]

Limit[Cosh[x]-Sinh[x],x-> ∞]

Limit[Cosh[x]-Sinh[x],x-> -∞]

Limit[Cos[Sin[x]]^(1/ArcSin[x]^2),x-> 0]

f[x_]:=a^x/(a^x+1)

Limit[f[x],x-> ∞,Assumptions-> 1>a>0]

Limit[f[x],x-> ∞,Assumptions-> 1<a]

Limit[f[x],x->- ∞,Assumptions-> 1>a>0]

Limit[f[x],x-> -∞,Assumptions-> 1<a]

Limit[(a^(x^2)-b^(x^2))/Log[Cos[2 x]],x-> 0,Assumptions-> (1>a>0)&&(1>b>0)]

Limit[(a^x-a^b)/((b x^2)^(1/3)-b),x-> b,Assumptions-> (a>0)&&(b>0)]

Limit[(a^x-a^b)/(-(Abs[b x^2])^(1/3)-b),x-> b,Assumptions-> (a>0)&&(b<0)]

<<NumericalCalculus`

a=2;b=-2;
NLimit[(a^x-a^b)/((b x^2)^(1/3)-b),x-> b]

Limit[((((-((Abs[x-6])^(1/3))+2))^2)/(((x^3)+8) ArcTan[x+2])),x-> -2]