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CC T1MP2 Quiz #1 Revie...
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to of tha himnatia
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Quiz #2 Review Sheet
Scholars' Academy
Date:
College Calculus
Class:
1) Determine if the following functions are continuous using the definition of continuity. If they are not
continuous, state where the discontinuities happen, why they fail the definition of continuity and what
type of discontinuity they are.
x' - 3.x +2
a) y -x? +4x-5
= (x-a)(x-1)
(x+5)(x-1)
Holo af x=/
VA ad X=-S
Not conhnvous at x=l as tuir is a removable
discontinuity and e (1) does not exist
Not continuous ad x- -5 as theis an infinite
ition w z)
b) y x3 +5x2 +6x
x'-4x discontinuity and f(-s) does not exist
Ex (X-4)
Not continuous at X-o,-2, -3 as
C
X(x 24 5x+()
f (o), f(-), and f(-3) do not exist,
Holo af
X=0,-2
= x (x-a)(x. 2)
There is removable di continuities at
X=0,-2 and infinite discontinuit
VA ad X=-3
x ( xta)( x+ 3)
x+1, x62 2+1= 3 7+0
at X- -3
SNE
c) f(x) =1x2-2, 2<x<4 Of Jump discontinuity at x=a sinu
(Vx+5 , x24
f(a) does not exist and Hy,
()'-a = 14
VA+S : 3>+
Jump discontinuity at x =4,
and linut f() DIE since
X-24
limfix) - 14
d) f (x) =
O if x = 3
2x2-18
x-3" if x + 3
and lin fux) = 3
2(x ?a)
-, Removable dis wonhnuity at x=3
C
(x-3)
-> Not continuous since f (2)=0
lime = alx43)
X-73
=la
How ad x=3
but Umf(x) = va, so
X-13
y= a(x+3)-a(313)ela
f(3) = kimfo
hik long)
2
2) Given the following graph of function, g(x),
a) Find all x values where the graph is discontinuous.
b) For each discontinuous x value, name the type of discontinuity.
c) For each discontinuous x value, state why it fails the formal definition of continuity.
d) Determine the intervals where the function is continuous....

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- Fall '16
- Ms. Grieco
- Continuous function, Classification of discontinuities, Theis, 4x-5