`lim_(x->oo) (1+ (4/(x-1)))^(x+3)`

lim_(xrarr oo) (1-(4)/(x-1))^(3x-1) is equal to

Match the following : {:("Column I ", " Column II" ), ("(A)" if lim_(x to 1) (1-x) tan""(pix)/2 = k " then " sin (1/k) " is" , "(p)"4),( "(B)" if lim_(x to 5) (x^(k)-5^(k))/(x-5) = 500 " then k is " , "(q)" 1),("(C)" lim_(x to oo)(1 + 4/(x+1))^((3x-1)/3) " is equal to " e^(k) " , then k is" , "(r) A perfect sqare"), ("(D) " d^(20)/(dx^(20)) (2 cos x"," cos 3x)= 2^(4k) [ cos2x + 2^(20) . cos4k]" then k is " , "(s)" 5),(, "(t)An odd number"):}

lim_(x->oo)sin(1/x)/(1/x)

lim_(xrarr oo) ((x+5)/(x-1))^(x) is equal to

The value of lim_(x->oo)(((x-1)(x-2)(x+3)(x+10)(x+15))^(1/5)-x) is ....

Evaluate : lim_(x to oo) ((x-3)/(x+3))^(x+3)

Evaluate the following limit: (lim)_(x->oo)((3x-1)(4x-2))/((x+8)(x-1))

lim_(x->oo)((1^(1/x) +2^(1/x) +3^(1/x) +...+n^(1/x))/n)^(nx) is equal to

lim_(x -> oo) ((x-3)/(x+2))^x is equal to

lim_(x->oo)(1-x+x.e^(1/n))^n