For what values of p does the `Lim_(x->1) f(x)` exist, where `f(x)` is defined by the rule `f(x)={(2px +3, if x <1) , (1-px^2, if x>1):} `

For what values of p does the Lim_(x to 1) f(x) exist , where f is defined by the rule f(x) = {:{(2px+3," if " x lt 1 ),(1 - px^(2)," if "x gt 1):}

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

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

verify the existence of lim_(x to 1) f (x) , where f(x) ={{:((|x-1|)/(x-1) , "for" x ne 1),(0 , ", for " x=1):}

Find lim_(x to 1) f(x) , where f(x) = {{:(x + 1, x != 1),(0, x = 1):}}

Find lim_(x to 1) f(x) , where f(x) = {{:(x + 1, x != 1),(0, x = 1):}}

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

Find lim_(x rarr 0)f(x) and lim_(x rarr 1) f(x) , where f(x)={(2x+3,xle0),(3(x+1),x>0):}

f(x)={(ax+2, x 1):} , If lim_(x rarr1)f(x) exist then value of a is :

Which of the following statement(s) is (are) INCORRECT ?. (A) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f(g(x)) also does not exist.(B) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f'(g(x)) also does not exist.(C) If lim_(x->c) f(x) exists and lim_(x->c) g(x) does not exist then lim_(x->c) g(f(x)) does not exist. (D) If lim_(x->c) f(x) and lim_(x->c) g(x) both exist then lim_(x->c) f(g(x)) and lim_(x->c) g(f(x)) also exist.