(1)` lim_(x->0)(3x+1)/(x+3)`

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

Compute (lim)_(x->0)(e^(3x)-1)/x

value of lim_(x->0)(1-cos^3x)/(xsinx*cosx) is

lim_(x→0) (√(x+1)−1)/x

Find the following limits: (i)lim_(xto0) (1)/(x)sin^(-1)((2x)/(1+x^(2)))" "(ii)lim_(xto0) (1)/(x)sin^(-1)(3x-4x^(3))

Let a= lim_(x->0)ln(cos2x)/(3x^2), b=lim_(x->0)(sin^(2)2x)/(x(1-e^x)), c=lim_(x->1)(sqrt(x)-x)/lnx

STATEMENT-1 : lim_(x->oo)(log[x])/([x])=0 . STATEMENT-2 : lim_(x->0)(sqrt(sec^2-1))/x does not exist. STATEMENT-3: lim_(x->2)(x-1)^(1/(x-2)) = 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

3) lim_(x rarr0)[(1)/(x)-cot x]

If lim_(x->0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(lim_(x->0)[1+(f(x))/x]^(1/x))i s____