Evaluate: `lim_(x->oo) (1+1/(a+bx))^(c+dx)` , where `a,b,c` and dare positive

Evaluate the following limits: (lim)_(x->oo)(1+1/(a+b x))^(c+dx)w h e r e\ a ,\ b ,\ c\ a n d\ d are positive.

Evaluate: lim_(x rarr oo)x^((1)/(x))

Evaluate: lim_(x rarr oo)[(x-1)/(x-2)]^x

Evaluate lim_(x to 0) (1 - cos ax)/(1 - cos bx)

Evaluate: lim_(x rarr oo)[x(a^((1)/(x))-1)],a>1

Evaluate :lim_(x rarr oo)(ax^(2)+bx+c)/(dx^(2)+ex+f)

int_(n in N)(a*x^(n-1))/(bx^(n)+c)dx where a,b,c are real nuber

If f(x)=a+bx^(2)+cx^(4)+dx^(6), where a,b,c,d all are positive constants, then

Let lim_(x rarr oo)x ln(e(1+(1)/(x))^(1-x)) equal (m)/(n) where m and n are relatively prime positive integ Find (m+n).

lim_(x rarr oo)a^(x)sin((b)/(a^(x))), where a>1, is equal to