`lim_(x-gt0)(sinalphax)/(tanbetax)`

lim_(xto0)(sinalphax)/(sinbetax)

Evaluate the following limits: lim_(xrarr0)(tan alphax)/(tanbetax)

lim_(xrarr0)(sinalphax)/(e^(betax)-1)(alpha,beta!=0) equals to

lim_(x->o)(e^(alphax)-e^(betax))/(sinalphax-sinbetax)

Prove : underset(xrarr0)"lim"(sinalphax^(@))/(sinbetax^(@))=(alpha)/(beta)

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

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

lim_(x-gt0) (xcot4x)/((cot^2 2x)(sin^2 x)) is equal to (A) 1 (B) 2 (C) 4 (D) 6

Statement-1 : lim_(x to 0) (1 - cos x)/(x(2^(x) - 1)) = (1)/(2) log_(2) e . Statement : lim_(x to 0) ("sin" x)/(x) = 1 , lim_(x to 0) (a^(x) - 1)/(x) = log a, a gt 0