Evaluate : `("lim")_(xvecoo)(a x^2+b x+c)/(dx^2+e x+f)dot`

Evaluate : lim_(x -> 0 ) ((e^(x^(2)) - cosx )) / x^2

Evaluate: (lim)_(x->0)log_(tan^2x)(tan^2 2x)dot

The value of (lim)_(xvecoo)[tan^(-1)(x+1)/(x+2)-dotpi/4],w h e r e[x] denotes greatest integer lt=x , is 1/2 b. -1/2 c.1 d. -1

Evaluate: lim_(x rarr0)(e^(x)+e^(-x)-2)/(x^(2))

Evaluate lim_(xrarr2)((e^(x)-e^(2))/(x-2)).

Evaluate lim_(xto0) (e^(x)-1-x)/(x^(2)).

If (lim)_(xvecoo)(2+(f(x))/(x^2))^(1/x)=e and f(x)=a_0+a_1x+a_2x^3+ , then

Evaluate: lim_(x rarr 2)(f(x)-f(2))/(x-2), "where" f(x)=x^(2)-4x

prove "lim"_(xvecoo)(ln x)/([x])="lim"_(xvecoo)([x])/(ln x) where [.] is G.I.F. & {.} denotes fractional part function

Evaluate: lim_(x rarr oo)((int_(0)^(x)e^(x^(2))dx)^(2))/(int_(0)^(x)e^(2x^(2))dx)