Notesale: Turn your study into money

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Math 135: Exam 𝟏 Review
For exercise 1-5, graph each function and then find the specified limits
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𝟏
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𝑥→3
𝑥→4
𝑥−3

𝟐
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𝑥→∞
𝑥→0
𝑥

𝟑
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;
𝑥→1−
𝑥→1
𝑥→1+
for 𝑥 ≥ 1

𝟒
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𝑥→3
𝑥→3
for 𝑥 > 3
𝑥→3

𝟓
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𝑥→0

𝑥→−2

6
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Is the function given by
𝑓 𝑥 =

1
2

𝑥 + 1,

for 𝑥 < 4
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continuous at 𝑥 = 4? Why or why not?
8
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continuous at 𝑥 = 3? Why or why not?
9
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Find 𝑠 5 − 𝑠 3
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What is the average rate of change of distance with respect to time during the period from 3
to 5 sec? (Hint: This is also known as average velocity
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At the beginning of a trip, the odometer on a car reads 30,680, and the car has a full tank of gas
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It takes 13
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a
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What is the average rate of gas consumption in gallons per mile?
For Exercise 11 and 12:
a
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Find 𝑓′ −2 , 𝑓′ 0 , and 𝑓′ 1
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𝑓 𝑥 = −2𝑥 2

ℎ→0

𝑓 𝑥+ℎ − 𝑓 𝑥

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𝑓 𝑥 = 2𝑥 + 3

13
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14
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For what 𝑥-value(s) is the function not differentiable?
b
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Is there a shortcut you can use to find these slopes?
15
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a
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b
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For Exercise 16-23, differentiate each function
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𝑦 = 3
2𝑥 + 3

𝟏𝟕
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𝐺 𝑥 = 8𝑥 +
𝟐𝟎
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𝐹 𝑥 = 𝑥 + 3

2

2

𝟐𝟏
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𝑓 𝑥 = 𝑥2 4𝑥 − 1

𝟐𝟑
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Summertime Fabrics finds that the cost, in dollars, of producing 𝑥 jackets is given by 𝐶 𝑥 =
950 + 15 𝑥
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25
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, finds that the cost, in dollars, of producing 𝑥 bottles of barbecue sauce
is given by 𝐶 𝑥 = 375 + 0
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Find the rate at which the average cost is changing when 81
bottles of barbecue sauce have been produced
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A total-revenue function is given by
𝑅 𝑥 = 1000

𝑥2 − 0
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Find the rate at
which total revenue is changing when 20 items have been sold
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Suppose that the demand function for a product is given by
80,000
,
𝑝
And that price 𝑝 is a function of time given by 𝑝 = 1
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a
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b
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𝐷 𝑝 =



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