`Lim_( x -> oo ) a^x = --- (if 0 < a < 1 )`

lim_(x rarr oo)a^(x)

lim_(x rarr-oo)e^(x)

lim_(x rarr oo)x^(3)

Let f : R to R be a function such that lim_(x to oo) f(x) = M gt 0 . Then which of the following is false?

A function f(x) having the following properties, (i) f(x) is continuous except at x=3 (ii) f(x) is differentiable except at x=-2 and x=3 (iii) f(0) =0 lim_(x to 3) f(x) to - oo lim_(x to oo) f(x) =3 , lim_(x to oo) f(x)=0 (iv) f'(x) gt 0 AA in (-oo, -2) uu (3,oo) " and " f'(x) le 0 AA x in (-2,3) (v) f''(x) gt 0 AA x in (-oo,-2) uu (-2,0)" and "f''(x) lt 0 AA x in (0,3) uu(3,oo) Then answer the following questions Find the Maximum possible number of solutions of f(x)=|x|

lf lim_(x to 0) (sin x)/( tan 3x) =a, lim_( x to oo) (sinx)/x =b , lim_( x to oo)( log x)/x = c then value of a + b + c is

underset x rarr oo lim_ (x rarr oo) ((x ^ (2) +1) / (x + 1) -ax-b) = 0 then find

lim_ (x rarr oo) ((x + 2) / (x-2)) ^ (x + 1)

lim_ (x rarr oo) (x + e ^ (x)) ^ ((2) / (x))

lim_ (x rarr oo) (x ^ (n)) / (e ^ (x)) = 0, (n is an integer) for