`("lim")_(xrarroo)(1/e-x/(1+x))^x` is equal to (a) `e/(1-e)` (b) 0 (c) `e/(e^(1-e))` (d) does not exist

lim_(nrarroo) (1-x+x.root n e)^(n) is equal to

For x in R , lim_(xrarroo)((x-3)/(x+2))^x is equal to (a) e (b) e^(-1) (c) e^(-5) (d) e^5

("lim")_(xvecoo)[(e/(1-e))(1/e-x/(1+x))]^xi s e^((1-e)) (b) e^(((1-e)/e)) (c) e^((e/(1-e))) (d) e^(((1+e)/e))

' lim_ (x to 0) (a^(x)-b^(x))/(e^(x)-1) is equal to

int_(-pi/2)^(pi/2)(e^(|sinx|)cosx)/(1+e^(tanx))dx is equal to (a) e+1 (b) 1-e (c) e-1 (d) none of these

Show that ("lim")_(xto0) (e^ (1/x)+1 / e^ (1/x)-1) does not exist

lim_(xto1)(e^(x)-e)/(x-1)= ……………

("lim")_(xvec1)[cos e c(pix)/2]^(1/((1-x)))(w h e r e[dot]r e p r e s e n t st h e gif is e q u a l to (a) 0 (b) 1 (c) oo (d) does not exist

The value of lim_(x rarr 1)(2-x)^(tan((pix)/2)) is (a) e^(-2/pi) (b) e^(1/pi) (c) e^(2/pi) (d) e^(-1/pi)