lii lim_(x rarr1)[x]

show that lim_(x rarr1)[2x+3]=5

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))

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 rarr1)([x])^((1)/(x-1))

Consider the function f(x)={(max(x,(1)/(x)))/(min(x,(1)/(x))),quad if x!=0 and 1,quad if x=0 then lim_(x rarr0){f(x)}+lim_(x rarr1){f(x)},lim_(x rarr1)[f(x)]=

Find value of a if lim_(x rarr1)(x^(4)-1)/(x-1)=lim_(x rarr a)(x^(3)-a^(3))/(x^(2)-a^(2))

Solve: (i) lim_ (x rarr1) [sin ^ (- 1) x]

Letf(x)={x+lambda,x =1 if lim_(x rarr1)f(x) exist,then find value of lambda