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Byju's Answer
Standard XII
Mathematics
Graph of Trigonometric Ratios
The nbsp;fu...
Question
The
function
f
(
x
)
=
sec
x
is
continuous
for
all
x
∈
R
.
A
False
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B
True
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Q.
The function
f
x
=
sin
π
x
-
π
4
+
x
2
, where [⋅] denotes the greatest integer function, is
(a) continuous as well as differentiable for all x ∈ R
(b) continuous for all x but not differentiable at some x
(c) differentiable for all x but not continuous at some x.
(d) none of these
Q.
If
f
x
=
log
e
|
x
|
, then
(a) f (x) is continuous and differentiable for all x in its domain
(b) f (x) is continuous for all for all × in its domain but not differentiable at x = ± 1
(c) f (x) is neither continuous nor differentiable at x = ± 1
(d) none of these
Q.
Let
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
for all x and y. If the function
f
(
x
)
is continuous at
x
=
0
, show that
f
(
x
)
is continuous for all x.
Q.
The
function
f
(
x
)
=
sec
x
is
continuous
for
all
x
∈
R
.
Q.
Let
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
for all
x
and
y
. If the function
f
(
x
)
is continuous at
x
=
0
, then
f
(
x
)
is continuous
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