Consider following statements and identify correct options (i) `lim_(x->4)((2x)/(x-2)-8/(x-4))=lim_(x->4)((2x)/(x-4))-lim_(x->4)(8/(x-4))`(ii) `lim_(x->1)((x^2+6x-7)/(x^2+5x-6))= (lim_(x->1)(x^2+6x-7) )/(lim_(x->1)(x^2+5x-6))`

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->4)(x-2)/(x-8)

lim_(x to 1)(x^(2)-6x+5)/(x^(2)+3x-4)=

Determine whether the statement is true or false lim_(x rarr4)((2x)/(x-4)-(8)/(x-4))=lim_(x rarr4)(2x)/(x-4)-lim_(x rarr4)(8)/(x-4)

Let f(x)=lim_(n->oo)(2x^(2n)sin(1/x)+x)/(1+x^(2n)) then find (a) lim_(x->oo) xf(x) (b) lim_(x->1) f(x) (c) lim_(x->0) f(x) (d) lim_(x->-oo) f(x)

lim_(x-gt0)(cos2x-cos3x)/(cos4x-1)

Find the limits (i) (lim)_(x->1)[(x^2+1)/(x+100)] (ii) (lim)_(x->2)[(x^3-4x^2+4x)/(x^2-4)]

lim_(x to 0) ((2x-3)(3x-4))/((4x-5)(5x -6))

lim_(x to 0) ((2x-3)(3x-4))/((4x-5)(5x -6))

Evaluate: lim_(x->oo)((x^2+x-1)/(3x^2+2x+4))^((3x^2+x)/(x-2))