For all `x in (0,1)` `e^x<1+x` (b) `(log)_e(1+x) x` (d) `(log)_e x > x`

For all x in (0, 1) (A) e^(x) lt 1+x (B) log_e (1+x) lt x (C) sin x gt x (D) log_(epsi) x gt x

The differential coefficient of f((log)_e x) with respect to x , where f(x)=(log)_e x , is (a)x/((log)_e x) (b) 1/x(log)_e x (c)1/(x(log)_e x) (d) none of these

lim_(x rarr oo)n^(2)(x^((1)/(n))-x^((1)/((n+1)))),x>0, is equal to (a)0(b)e^(x)(c)(log)_(e)x(d) none of these

int _(1) ^(e ) (dx )/(ln (x ^(x) e ^(x)))

int_(1)^(e )x^(x)dx+ int_(1)^(e )x^(x)log x dx=

(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)

(d)/(dx)(log e^(x)*log x)

The value of int_(1)^(e)((tan^(-1)x)/(x)+(log x)/(1+x^(2)))dx is tan e(b)tan^(-1)e tan^(-1)((1)/(e))(d) none of these

The differentiation of log _(e)x,x>0is(1)/(x)* i.e.(d)/(dx)(log_(e)x)=(1)/(x)

The differentiation of log_(a)x(a>0,a)*!=1 with respect to x is (1)/(x log_(a)a) i.e.(d)/(dx)(log_(a)x)=(1)/(x log_(a)a)