Let `f(x)={a x+b if x >1 ,3b x-2a+1 if x<1` Find a relation between a and b so that `lim_(x->1)f(x)` exists.

Let f(x)={x+1,\ if\ x >0, and x-1,\ if\ x 1)\ f(x) does not exist.

Let f(x)={{:(x^(2)+1,, x 2) :} and lim_(xrarr2)f(x) exist, then the value of k is Select one: a. (1)/(2) b. 5 c. 4 d. 3

Let f(x) = 2x^(2) + 5x + 1 . If we write f(x) as f(x) = a (x + 1) (x - 2) + b(x-2) (x - 1) + c(x - 1) (x +1) for real numbers a , b, c then

Let f(x)={1+(2x)/a ,0lt=x 1)f(x) exists ,then a is (a) 1 (b) -1 (c) 2 (d) -2

Let f(x)={a x^2+1,\ \ \ \ \ x >1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1 Then, f(x) is derivable at x=1 , if a=2 (b) b=1 (c) a=0 (d) a=1//2

Let f(x)={a x^2+1,\ \ \ \ \ x >1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1 Then, f(x) is derivable at x=1 , if a=2 (b) b=1 (c) a=0 (d) a=1//2

For all x in [1, 2] Let f"(x) of a non-constant function f(x) exist and satisfy |fprimeprime(x)|<=2. If f(1)=f(2), then (A) There exist some a in (1,2) such that f'(a)=0 (B) f(x) is strictly increasing in (1,2) (C) There exists atleast one c in (1,2) such that f'(c)>0 (D) |f'(x)| lt 2 AA x in [ 1,2]

For all x in [1, 2] Let f"(x) of a non-constant function f(x) exist and satisfy |fprimeprime(x)|<=2. If f(1)=f(2) , then (A) There exist some a in (1,2) such that f'(a)=0 (B) f(x) is strictly increasing in (1,2) (C) There exists atleast one c in (1,2) such that f'(c)>0 (D) |f'(x)| lt 2 AA x in [ 1,2]

Let f:Rto(-1,1) be defined by f(x)=x/(1+x^2),x in R . Find f^(-1) if exists.