8. `lim_(x->00)(1+a/x)=`

Which of the following limits does not exist ?(a) lim_(x->oo) cosec^(-1) (x/(x+7) (B) lim_(x->1) sec^(-1) (sin^(-1)x) (C) lim_(x->0^+) x^(1/x) (D) lim_(x->0) (tan(pi/8+x))^(cotx)

Use formula lim_(x->0)(a^x-1)/x=log(a) to find lim_(x->0)(2^x-1)/((1+x)^(1/2)-1)

lim_(x->0) ((1+x)^(1/x)-e)/x is equal to

Evaluate: lim_(x->0)(e-(1+x)^(1/x))/x

lim_(x->0)(1/(x^2)-1/(tan^2x))

Let f(x)=x+sqrt(x^2+2x) and g(x)=sqrt(x^2+2x-x) , then which of the following is/are true. a. lim_(x->oo)g(x)=1 b. lim_(x->oo)f(x)=1 c. lim_(x->oo)f(x)=-1 d. lim_(x->oo)g(x)=-1

Evaluate: lim_((x,y)->(0,0))(x^(3)y)/(x^(4)+y^(4))

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____

lim_(x->oo)sin(1/x)/(1/x)

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