_________.
2
1
∞
0
Ltx → 0 f ( x ) / g ( x ) exists, then
Both lim x → a f (x ) and lim x → a g ( fx ) must exist
lim f ( x ) need not exist but lim g (x ) exists x → a x → a
Nither lim f ( x ) nor lim g ( x ) does not exist. x → a x → a
lim f (x ) exists but lim g ( x ) does not exist. x → a x → a
The domain of th function where [x ] denotes the greatest integer less than or equal to x, is ______
(0, ∞ )
(-∞, 0)
( -∞, ∞ )
None of these
A function y = f ( x ) is said to even if _______.
f ( - x ) = - f (x )
f ( -x ) = f ( x )
f ( x ) = - f ( x )
f ( x ) = f ( x )
Ltx → 2+ [x] is equal to ________.
-1
f ( x ) = x x is rational = 1 - x if x is irrational, then
f is only right continuous at x = 1/2
f is only left continuous at x = 1/2
f is continuous at x = 1/2
f is discontinuous at all points
The range of the function is.
( -∞, - 1/4 )
R - { - 1/4, - 1/ 20 }
[ - 1/20, ∞ )
Let f : A →B and A R and B R be defined by y = f (x ), where x A, Y B, then f is called ______.
Real function
Into function
One - One function
None
If f ( x ) = x sin 1/x; x ≠ 0 = k; x = 0.is continuous at x = 0, then the value of k is ________.
lim f ( x ) x → a+ = l = ltx → a - g( x ) and Ltx → a - f ( x ) = m = Lt x → a + g ( x ), then the function f ( x ). g ( x )
Is continuous at x = a
Is not continuous at x = a
Has a limit when x → a and it is equal to lm
Has a limit when x → a + bvut it is nto equal to lm
