`lim_(x-gt0)(a^(3x)-b^(4x))/(5x)`

lim_(x-gt0) (e^(3x)-1)/(log(1+5x))

lim_(x->0)(e^(5x) - 1)/(3x)

lim_(x->0)(e^(5x) - 1)/(3x)

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

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

lim_(x rarr0)(x(5^(x)-3^(x)))/(cos2x-cos4x)

lim_(x to 0) ((2x-3)(3x-4))/((4x-5)(5x -6))