40 Part I: The Questions
264. f x
x
x
x
x
x
x
( ) =
−
≤
−
< ≤
+
<
2
2
4 2
3
1
5
3
2
where a = 2 and a = 3
265. f x
x
x
x
x
x
x
( )
cos
=
≤
< ≤
+
<
0
1
0
4
2
4
4
where a = 0 and a = 4
Making a Function Continuous
266–267 Determine the value of c that makes the
given function continuous everywhere.
266. f x
cx
x
cx
x
( ) =
−
≤
+
<
2
2
1 2
2
267. f x
x c x
cx
x
( ) =
+
≤
+
<
2
2
4
12 4
260. f x
x
x
x
x
( ) =
+
+
≠ −
−
=−
6
6
6
1
6
where a = –6
261. f x
x
x
x
x
( ) =
+
+
≠ −
= −
3
1
1
1
2
1
where a = –1
262–265 Determine whether the function is
continuous at the given values of a. If it isn’t
continuous, classify each discontinuity as a jump,
removable, or infinite discontinuity.
262. f x
x
x
x
x
x
x
( )
cos
sin
=
+
≤
< ≤
−
<
2
0
2
0
2
2
π
π
where a = 0 and a = π
263. f x
x
x
x
x
x
x
( ) =
+
≤
< ≤
<
2
1
2
1
3
3
2
3
where a = 1 and a = 3
264. f x
x
x
x
x
x
x
( ) =
−
≤
−
< ≤
+
<
2
2
4 2
3
1
5
3
2
where a = 2 and a = 3
265. f x
x
x
x
x
x
x
( )
cos
=
≤
< ≤
+
<
0
1
0
4
2
4
4
where a = 0 and a = 4
Making a Function Continuous
266–267 Determine the value of c that makes the
given function continuous everywhere.
266. f x
cx
x
cx
x
( ) =
−
≤
+
<
2
2
1 2
2
267. f x
x c x
cx
x
( ) =
+
≤
+
<
2
2
4
12 4
260. f x
x
x
x
x
( ) =
+
+
≠ −
−
=−
6
6
6
1
6
where a = –6
261. f x
x
x
x
x
( ) =
+
+
≠ −
= −
3
1
1
1
2
1
where a = –1
262–265 Determine whether the function is
continuous at the given values of a. If it isn’t
continuous, classify each discontinuity as a jump,
removable, or infinite discontinuity.
262. f x
x
x
x
x
x
x
( )
cos
sin
=
+
≤
< ≤
−
<
2
0
2
0
2
2
π
π
where a = 0 and a = π
263. f x
x
x
x
x
x
x
( ) =
+
≤
< ≤
<
2
1
2
1
3
3
2
3
where a = 1 and a = 3