Which of the following function is periodic in R ?
f ( x ) = log x
f ( x )= ex
f (x ) = x - [x ] where [ x ] denotes the greatst integer ≤ x
f ( x ) = [ x ] + x
Which of the following is false ?
| x + y | ≤ | x | + | y |
| x + y | ≥ | x | - | y |
| x - y | ≤ | x | + | y |
| x - y | ≤ | x | - | y |
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
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
If f1 (x ) and f2 (x ) are defined on domains D1 and D2 respectively; then the domain of f1 ( x ) + f2 (x ) is _______.
D1 - D2
D1 ∩ D2
D1 D2
D2 - D1
0
-1
1
∞
-π
π
π/2
_________.
2
3
8
3/2
2/3
1/6
6
