lim_(x rarr((x+6)/(x+1))))^(x+4)-

lim_(x rarr oo) ((x+6)/(x+1))^(x+4) =

lim_(x rarr0)((tan x)/(x))^(1/x)

lim_(x rarr oo) ((x + 6)/(x + 1))^(x + 4) is :

COnsider the following statements and identify the correct options ( i ) lim_(x rarr4)((2x)/(x-4)-(8)/(x-4))=lim_(x rarr4)(2x)/(x-4)-lim_(x rarr4)(8)/(x-4) (ii) lim_(x rarr1)(x^(2)+6x-7)/(x^(2)+5x-6)=(lim_(x rarr1)(x^(2)+6x-7))/(lim_(x rarr1)(x^(2)+5x-6))

lim_(x rarr0)((6^(x)+5^(x)+4^(x)-3^(x+1))/(sin x))

Consider following statements and identify correct options (i) lim_(x rarr4)((2x)/(x-2)-(8)/(x-4))=lim_(x rarr4)((2x)/(x-4))-lim_(x rarr4)((8)/(x-4)) (ii) lim_(x rarr1)((x^(2)+6x-7)/(x^(2)+5x-6))=(lim_(x rarr1)(x^(2)+6x-7))/(lim_(x rarr1)(x^(2)+5x-6))

lim_(x rarr0)(4^(x)-e^(x))/(6^(x)-1)

lim_ (x rarr oo) ((x + 1) ^ (4) - (x-1) ^ (4)) / ((x + 1) ^ (4) + (x-1) ^ (4))

lim_(x rarr oo)(1+4/(x-1))^(x+3) =