`lim_(x->0)(logtan2x)/(logtanx)`

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

lim_ (x-> 0) (log (a + x) -loga) / x + klim_ (x-> e) (logx-1) / (xe) = 1 then

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->0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)= (a) -1 (b) 1 (c) 0 (d) 2

lim_(x->0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)= (a) -1 (b) 1 (c) 0 (d) 2

lim_(x-gt0)(cos2x-cos3x)/(cos4x-1)

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

Evaluate Lim_(x to 0) (log (a+x) - log(a-x))/x , a gt 0

int(logtanx)/(sin2x)dx :

(i) lim_(x to 0) (a^(x) - 1)/(log_(a)(1 + x)), a gt 0 (ii) lim__(x to 0) (In (X + a)- In a)/(e^(2x) - 1) (ii) lim_(x to (pi)/(4)) (In(tanx))/(1 - cotx)