Always,
Sometimes,
or Never True
Solve for x
Limits
Derivatives
10
10
10
10
20
20
20
20
30
30
30
30
40
40
40
40
50
50
50
50
Click here for game DIRECTIONS
Hardtke Jeopardy Template 2011
10
Always, Sometimes, or Never
lim 𝑓(𝑥)
𝑓(𝑥)
𝑥→𝑎
lim
=
𝑥→𝑎 𝑔(𝑥)
lim 𝑔(𝑥)
𝑥→𝑎
Click to check answer
SOMETIMES
Hint: Not true if lim 𝑔 𝑥 = 0 .
𝑥→𝑎
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20
Always, Sometimes, or Never
A rational function f has
an infinite discontinuity.
Click to check answer
SOMETIMES
Hint: it might have only a removable discontinuity.
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30
Always, Sometimes, or Never
x
e
For f(x) =
as x ∞ , f(x)  0.
Click to check answer
NEVER
Hint: As x  ∞, f(x)  ∞
As x  - ∞, f(x)  0
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40
Always, Sometimes, or Never
lim 𝑓(𝑥) = 𝑓(𝑎).
𝑥→𝑎
Click to check answer
SOMETIMES
Hint: true when f is continuous at a.
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50
Always, Sometimes, or Never
If f(0) = -3 and f(5) = 2, then
f(c) = 0 for at least one
value of c in (-3, 2).
Click to check answer
SOMETIMES
Hint: IVT will prove this true only if is continuous over
that interval.
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10 Solve for n
f(x) =
2
𝑥 −𝑥−6
has
an
infinite
𝑥 2 −4
discontinuity at n.
Click to check answer
2
(𝑥−3)(𝑥+2)
Hint: f(x) =
has a
(𝑥−2)(𝑥+2)
removable discontinuity at -2 and an infinite discontinuity at 2.
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20
Solve for n
f is continuous for this value of n.
𝑛𝑥 + 𝑛 𝑥 < 4
𝑓 𝑥 =
3𝑥 + 𝑛 𝑥 ≥ 4
Click to check answer
3
Hint: 4n + n = 12 + n when n = 3
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30
Solve for n
2
25𝑥 −3
For f(x) =
𝑥 + 34
as x  – ∞ , f(x) n
Click to check answer
–5
As x  – ∞ , f(x) ≈
| 5𝑥 |
𝑥
–5
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40
lim
Solve for n
3
𝑥 −64
2 −5𝑥+4
𝑥
𝑥 →4
=n
Click to check answer
16
(𝑥−4)(𝑥 2 + 4𝑥 +16)
lim
(𝑥−4)(𝑥−1)
𝑥 →4
=
48
3
=16
Click to return to game board
50
Solve for n
Given polynomial function f, where
f(8) = -2 and f(-2) = 3, then there
exists at least one value of c ∈ (-2, n)
such that f(c) = 0.
Click to check answer
𝟖
Hint: By IVT there must be an x-coordinate between -2 and
8 that produces a y-coordinate between -2 and3.
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10
Limits
2𝑥−1
3𝑥 3
Given 𝑓 𝑥 =
Find lim 𝑓 𝑥 .
𝑥 →0
Click to check answer
d.n.e.
As x → 0 -, f(x) → ∞. As x → 0 +, f(x) → - ∞
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20
Limits
𝑥−3
𝑥−3
Given 𝑓 𝑥 =
𝐹𝑖𝑛𝑑 lim 𝑓 𝑥 .
𝑥 →3−
Click to check answer
-1
lim 𝑓 𝑥 = −1 𝑎𝑛𝑑 lim 𝑓 𝑥 = 1 .
𝑥 →3−
𝑥 →3+
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30
lim
𝑥 →0
Limits
𝑥 + 25 − 5
=?
𝑥
Click to check answer
𝟏
𝟏𝟎
𝑥 + 25 − 5 𝑥 + 25 + 5
lim
∙
𝑥 →0
𝑥
𝑥 + 25 + 5
Click to return to game board
40
Limits
sin 7𝑥
lim
𝑥 →0 3𝑥
Click to check answer
𝟕
𝟑
7
sin 7𝑥
lim
3 𝑥 →0 7𝑥
=
7
(1)
3
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50
Limits
𝑥
𝑒 +2
lim
𝑥
𝑥 →− ∞ 3𝑒 − 4
Click to check answer
𝟐
𝟏
=−
−𝟒
𝟐
Click to return to game board
10
Derivatives
𝑑 𝑛
𝑥 =?
𝑑𝑥
Click to check answer
n-1
nx
Hint: This is the Power Rule
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20
Derivatives
𝑓′ 𝑥 > 0 only on intervals
where f(x) is ____.
Click to check answer
𝒊𝒏𝒄𝒓𝒆𝒂𝒔𝒊𝒏𝒈
Hint: rising or going up or has a positive slope are acceptable
but not as nice
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30
Derivatives
3
3
2+ℎ −2
lim
ℎ→0
ℎ
Click to check answer
12
Hint: for f(x) = x3, you must recognize this as f ‘ (2)
where f ‘(x) = 3x2 and thus f ‘(2x) = 3(4) = 12
Click to return to game board
40
Derivatives
3
−4
𝑑 6𝑥 + 2𝑥
𝑑𝑥
2𝑥
− 8𝑥
Click to check answer
−𝟔
𝟔𝒙 − 𝟓𝒙
Hint: divide first then use Power Rule on each
𝑑
term 
(3𝑥 2 + 𝑥 −5 − 4)
𝑑𝑥
Click to return to game board
50
Derivatives
𝑑
𝑑𝑥
5
3
𝑥
𝑥
=?
Click to check answer
𝟏 −𝟗
𝒙 𝟏𝟎
𝟏𝟎
Hint: Subtract exponents first.
𝑑
𝑑𝑥
3
𝑥5
1
𝑥2
Click to return to game board
=
1
𝑑
𝑥 10
𝑑𝑥
=?
Jeopardy Directions
• Any group member may select the first question and students rotate choosing the
next question in clockwise order regardless of points scored.
• As a question is exposed, EACH student in the group MUST write his solution on
paper. (No verbal responses accepted.)
• The first student to finish sets down his pencil and announces “15 seconds” for all
others to finish working.
• After the 15 seconds has elapsed, click to check the answer.
– IF the first student to finish has the correct answer, he alone earns the point value of the
question (and no other students earn points).
– IF that student has the wrong answer, he subtracts the point value from his score and
EACH of the other students with the correct answer earns/steals the point value of the
question. (Those students do NOT lose points if incorrect, only the first student to “ring
in” can lose points in this version of the game.)
• Each student should keep a running total of his own score.
• Good sportsmanship and friendly assistance in explaining solutions is expected!
Reviewing your math concepts is more important than winning.
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