Miami University Calculating Limits Using the Limit Laws Problems

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1. [-/6 Points]
DETAILS
SCALCET9 2.3.001.
Given that
lim f(x) = 4
lim g(x) = -2
lim h(x) = 0,
X 1
X→ 1
x 1
find each limit, if it exists. (If an answer does not exist, enter DNE.)
(a) lim [F(x) + 49(x)]
X-1
(b) lim [g(x)]
X=1
(c)
lim F(x)
X-1
(d) lim
5f(x)
x-1 g(x)
(e) lim g(x)
x-1 h(x)
(f)
lim
x1
g(x)h(x)
f(x)
Na Land
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2. [-16 Points]
DETAILS
SCALCET9 2.3.002.
The graphs of fand g are given. Use them to evaluate each limit, if it exists. (If an answer does not exist, enter DNE.)
у
у
y=f(x)
y=g(x)
1
Wh
► x
1
(a) lim [f(x) + g(x)]
X→2
(b) lim [f(x) = g(x)]
x-0
(c)
lim [F(x)g(x)]
x-1
F(X)
(d) lim
X-3 g(x)
(e) im, x?F(x)]
X2
(f) f(-1) + lim g(x)
X-1
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3. [-11 Points]
DETAILS
SCALCET9 2.XP.3.002.
Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.)
lim (4×3 – 2x² +
+ x – 4)
x 3
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4. [-/1 Points]
DETAILS
SCALCET9 2.XP.3.005.
Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.)
A – 2
lim
t -2 21²
3t + 5
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5. [-/1 Points]
DETAILS
SCALCET9 2.XP.3.006.
Evaluate the limit using the appropriate Limit Law(s), (If an answer does not exist, enter DNE.)
lim vu
04
+ 30 + 15
07-5
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6. [-/1 Points]
DETAILS
SCALCET9 2.XP.3.007.
Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.)
lim (2 + x)(4 – 5×2 + x)
+
X8
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7. [-/1 Points]
DETAILS
SCALCET9 2.XP.3.008.
Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.)
lim
t-2
+2
2
– 7
23 – 8t + 6.
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8. [-/1 Points]
DETAILS
SCALCET9 2.XP.3.009.
Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter. DNE.)
lim
5x² + 5
5x – 1
X-2
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9. [-12 Points]
DETAILS
SCALCET9 2.3.010.
(a) What is wrong with the following equation?
x2 +
+ x – 42
= x + 7
X – 6
O (X – 5)(x + 7) = x2 + + X – 42
O The left-hand side is not defined for x = 0, but the right-hand side is.
O The left-hand side is not defined for x = 6, but the right-hand side is.
O None of these – the equation is correct.
(b) In view of part (a), explain why the following equation is correct.
x² + x
lim
EX- 42
lim
(x + 7)
X 6
x – 6
X 6
x² + x – 42
+ X
Since
and x + 7 are both continuous, the equation follows.
X – 6
Since the equation holds for all x + 6, it follows that both sides of the equation approach the same limit as x — 6.
O This equation follows from the fact that the equation in part (a) is correct.
O None of these – the equation is not correct.
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10. [-/1 Points]
DETAILS
SCALCET9 2.XP.3.012.
Find the limit. (If an answer does not exist, enter DNE.)
x² – 9x + 18
lim
X 3 x – 3
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11. [-/1 Points]
DETAILS
SCALCET9 2.3.021.MI.
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)
(h – 4)2 – 16
lim
h – 0
h
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12. [-16 Points]
DETAILS
SCALCET9 2.XP.3.015.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the
Tutorial Exercise
Find the limit.
lim (8 + h) 3 – 512
h-0
h
Click here to begin!
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13. [-/1 Points]
DETAILS
SCALCET8 2.3.020.
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.).
4 + h – 2
lim
h – 0
h
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14. [-/1 Points]
DETAILS
SCALCET9 2.3.028.
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)
1 (
(-
lim
t-0
t
2 + t
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15. [-/6 Points]
SCALCET9 2.3.037.
A graphing calculator is recommended.
Use the Squeeze Theorem to show that lim x2 cos(19nx) = 0.
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[-16 Points]
DETAILS
SCALCET9 2.3.037.
MY NOTES
ASK YOUR TEACHER
A graphing calculator is recommended.
Use the Squeeze Theorem to show that lim x2 cos(191x) = 0.
X-0
Illustrate by graphing the functions f(x) = -x?, g(x) = x2 cos(191x), and h(x) = x2 on the same screen.
Let f(x) = -x2, g(x) = x2 cos(191x), and h(x) = x2. Then ? vs cos(191x) 2M 12v
sx? cos(197x)
Since lim f(x) = lim h(x) =
X-0 X-0
by the Squeeze Theorem we have lim g(x) =
X-0
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16. [-/1 Points]
DETAILS
SCALCET9 2.3.039.MI.
F
MY NOTES
ASK YOUR TEACHER
If 3x – 4 s f(x) S x2 – 3x + 5 for x 20, find lim f(x).
X-3
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MY NOTES
ASK YOUR TEACHER
PRA
17. [-/1 Points]
DETAILS
SCALCET9 2.3.040.
If 2x 5 g(x) s x4 – x2 + 2 for all x, evaluate tim g(x).
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Math Problems

Calculating Limits

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