`lim_(x-gt0)(log(1+x^3)/(sin^3x)`

Find limit of the following if it exists: lim_(xto0)(log(1+x^(3)))/(sin^(3)x)

Evaluate the limits, if exist (lim)_(xrarr0)(log(1+x^3))/(sin^3x)

Evaluate the limits, if exist lim_(x-gt0)(log_e(1+2x))/(x)

Prove that: lim_(xto0)log(1+2x)/(sin3x)=(2)/(3)

Prove that lim_(x rarr 0) (log(1+x^3))/(sin^3 x)=1 .

Evaluate the limits,if exist (lim)_(x rarr0)(log(1+x^(3)))/(sin^(3)x)

Show that, lim_(x rarr 0) log(1+x^(3))/(sin^(3)x) = 1

Which of the following is/are true? (a) lim_(x->oo)((2+x)^(40)(4+x)^5)/((2-x)^(45))=1 (b) lim_(x->0)(1-cos^3x)/(xsinxcosx)=3/2 (c) lim_(x->0)(ln(1+2x)-2"ln"(1+x))/(x^2)=-1 (d) lim_(x->oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(sec^1((2x+1)/(x-1)^2)=1

Evaluate the following limit : (lim)_(x->0)((4^x-1)^3)/(sin((x^2)/4)log(1+3x))