`lim_(x->-1)[([x])/x]=`

lim_(x->0)(3^x-1)/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____

Let Lim_(x rarr1)([x])/(x)=l and lim_(x rarr1)(x)/([x])=m where [ .] denotes the greatest integer function, then

(lim)_(x->-1)(x^(10)+x^5+1)/(x-1)

If (lim)_(x->a)(x^3-a^3)/(x-a)=(lim)_(x->1)(x^4-1)/(x-1) , find all possible value o adot

If the function f(x) satisfies (lim)_(x->1)(f(x)-2)/(x^2-1)=pi, evaluate (lim)_(x->1)f(x)

Evaluate : lim_(x to -1) x/([x])

Consider the function f(x)={(max(x,(1)/(x)))/(min(x,(1)/(x))),quad if x!=0 and 1,quad if x=0 then lim_(x rarr0){f(x)}+lim_(x rarr1){f(x)},lim_(x rarr1)[f(x)]=

Find the limits: (i) (lim)_(x->1)[x^3-x^2+1] (iii) (lim)_(x->3)[x(x+1)] (iii) (lim)_(x->1)[1+x+x^2+. . . . .+x^(10)]

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