" (3) "a=-7,d=(1)/(2)rarr0

1.lim_(x rarr0)(cos2x-1)/(cos x-1)(2).lim_(x rarr0)(1-cos2mx)/(1-cos2nx)

L_(1)=lim_(x rarr0^+)(1+x)^(1/x),L_(2)=lim_(x rarr0^(+))(1+x)^(1/x^(2)),L_(3)=lim_(x rarr0^(+))(1+x^(2))^(1/x) ,Then

Evaluate lim_(x rarr 0) (e^(bx) - 1)/x and lim_(x rarr 0) (e^(ax) - 1)/x

Show that (lim)_(x rarr0)(1)/(2) does not exist.

If we assume u = tan^-1 2x , prove that lim_(x rarr 0) x/(tan^-1 2x) = 1/2 lim_(u rarr 0) (tan u)/u

Statement I: lim_(x rarr0)(x)/(sin b^(2)x)=4 then b=+-(1)/(2) Statement II: lim_(x rarr0)(sin x)/(x)=1

find the the value of lim_(x rarr 0) (e^(3x)-1)/(2x) and lim_(x rarr 0) log(1+4x)/(3x)

If l = underset( x rarr 0) ("Lim")( x ( 1+ a cos x ) - bsin x ) /( x^(3))= underset( x rarr 0 ) ("Lim") ( 1+a cos x ) /( x^(2))- underset( x rarr 0 ) ("lim")( b sin x )/( x^(3)) , where l in R , then

lim_ (x rarr0) (1) / (1-e ^ ((1) / (x))) =

If lim_(x rarr0^(+))f(x)=p and lim_(x rarr0^(-))f(x)=q then the corrects statement (s) is/are true?