" (ii) "(e^(x)+sin x)/(1+log_(e)x)

If x^(y) = e^(x - y) prove that (dy)/(dx) = (log_(e)x)/((1 + log_(e)x)^(2)) .

int_1^(e^(17)) (pi sin (pi log_(e)x))/(x)dx equals :

Which pair of functions is identical? (a)sin^(-1)(sinx) ,sin(sin^(-1)x) (b) log_(e)e^(x),e^(log_(e)x) (c) log_(e)x^(2),2log_(e)x (d)None of the above

For all x in (0,1) (a) e^x (b) (log)_e (1+x) (c) sin x > x (d) (log)_e x > x

int(1)/(1+e^(x))dx= (a) log(1+e^(x)) (b) log((1+e^(x))/(e^(x))) (c) log(1+e^(-x)) (d) -log(e^(-x)+1)

If (dy)/(dx)-y log_(e) 2 = 2^(sin x)(cos x -1) log_(e) 2 , then y =

If (dy)/(dx)-y log_(e) 2 = 2^(sin x)(cos x -1) log_(e) 2 , then y =

If (dy)/(dx)-y log_(e) 2 = 2^(sin x)(cos x -1) log_(e) 2 , then y =

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

(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)