Evaluate :
`lim_( x -> 1 ) f( 2x + 1 )`

Evaluate: lim_(x rarr 1) (f(x)-f(1))/(x-1), "where" f(x) = x^(2)-2x .

Evaluate: lim_(x rarr 1) [(x^(4)-2x^(3)-x^(2)+2x)/(x-1)] .

Evaluate lim_(x to 1) (x^3-1)/(x^2-1)

Evaluate lim_(x rarr1)(f(x)-f(1))/(x-1), where f(x)=x^(2)-2x

If f(x) is defined as f(x){{:(x,0lexlt(1)/(2)),(0,x=(1)/(2)),(1-x,(1)/(2)ltxle1):} then evaluate : lim_(xrarr(1)/(2)) f(x)

If f(x) is defined as f(x)={{:(2x,+,3,x,le 0),(3x,+,3,x,le0):} then evaluate : lim_(xrarr0) f(x) "and" lim_(xrarr1) f(x)

Evaluate: lim_(x rarr0)(1)/(x)sin^(-1)((2x)/(1+x^(2)))

f(x)={(x+1,; xlt1), (2x-3,; xgeq1):}, evaluate lim_(x rarr 1)f(x).

If the function f(x) satisfies lim_(x rarr1)(f(x)-2)/(x^(2)-1)=pi evaluate quad lim_(x rarr1)f(x)

Statement - 1: The function f(x) = {x}, where {.} denotes the fractional part function is discontinuous a x = 1 Statement -2: lim_(x->1^+) f(x)!= lim_(x->1^+) f(x)