`(lim)_(xvecoo)[x-log_e((e^x+e^(-x))/2)]=` `(log)_e4` b. 0 c. `oo` d. `(log)_e2`

lim_(xrarroo) [x-log_(e)((e^(x)+e^(-x))/(2))]=

(d)/(dx)[log((e^(4x))/(1+e^(4x)))]

lim_(x rarr0)(e^(x)-log_(e)(ex+e))/(x)

lim_ (x rarr oo) (log_ (e) x) / (x)

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

lim_( x to 1) {log_e (e^(x(x-1))-e^(x(1-x))) - log_e(4x(x-1))} is equal to :

(lim)_(x rarr oo)a^(x)sin((b)/(a^(x))),a,b>1 is equal to bb*ac.a(log)_(e)d.b(log)_(e)a

(d)/(dx)log_(7)(log_(7)x)= (a) (1)/(x log_(e)x) (b) (log_(e)7)/(x log_(e)x) (c) (log_(7)e)/(x log_(e)x) (d) (log_(7)e)/(x log_(7)x)

lim_(x rarr oo)(x-ln cosh x) where e osh t=(e^(t)+e^(-t))/(2)

Find the range of f(x)=log_(e)x-((log_(e)x)^(2))/(|log_(e)x|)