Chapter 1. Calculus Tutorial 2.1.007

1.1 Prelude to Section 1 (SM testing)

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eval rand(5,17,2)

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Question 1.1 Test question.

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2
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Question 1.2 New question

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UThjyvT6D5k8Ejv3msuGWNTrHBEqbDRXIzeQZfwr9R8= cell4
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1.2 Step 1

The rate of change of f(t) is the ratio of the change in f(t) divided by the unit change in t.

Question Sequence

Question 1.3

The account balance f(t) is measured in JvMTWtHHPxcVgRd4iHmpHpAOkxQe6GvTNzwj4lqqJTw= and t is measured in EFBAAtjIr6f0KWQKxGhjyzhRKP+ZNnARzqfy/+h/RGY=.

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2

Question 1.4

NUPwnHI1PVDtD3aarsmmuBpQ6ozv/Rm2/3eGZPEdwdKhQnCgv+17y2PFf7h1IOsrhkxJVHiFMQPXmkgMJnj4R+9GRJWimBgA5dzoT+YCPyZMS0NKHw6WVntg7VyjaSWMBEEOF4VHzHY86Hum9XWAMsky/IgLIKW8KLzaA5WWv3tsEYa1Mg7aGHEmTWJ/6ZbM1EdAitQYLHdVRya9r9611M1mPQ55gKDFveIpgA==
2
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1.3 Step 2

The average rate of change of y = f(t) over the interval [t0, t1] is given by the following.

Average rate of change =

Find the average rate of change over the interval [0, 0.5]. (Round your answers to two decimal places.)

Question Sequence

Question 1.5

For the interval [0.0, 0.5], let t0= 0 and t1 = ot+qaZUmHUo=.

2
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Question 1.6

In this case, f(t1) = 100*(iSba6t70dtA=

2
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Question 1.7

Thus the average rate of change is ogclm5qspRNIZA6hUagrKN0l3ew=.

2
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1.4 Step 3

Find the average rate of change over the interval [0, 1]. (Round your answers to two decimal places.)

Question Sequence

Question 1.8

For the interval [0, 1], let t0= 0 and t1 = 0VV1JcqyBrI=.

In this case, f(t1) = 100*(FB:*$b)1 and f(t0) = 100*(FB:*$b)0

2
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Question 1.9

Thus the average rate of change is FB:*$avgroc00to10.

2
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1.5 Step 4

Recall that the instantaneous rate of change at t = t0 is the limit of the average rates of change.

Question Sequence

Question 1.10

To estimate the instantaneous rate of change of the given problem, we calculate the average rate of change over smaller and smaller intervals to the nO/+DAdRVq+2oOvmzNgeN0ocEUKz3yEuOTAqpssC58Q= of t = ot+qaZUmHUo=

2
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Question 1.11

First calculate the average rate of change over three intervals to the right of t = 0.5. (Round your answers to four decimal places.)

Interval [0.5, 0.51] [0.5, 0.501] [0.5, 0.5001]
Average rate of change KM4Y0fTBDKXkN24kA9uYBg== tOpUvmG3/QKqNS+t06QXwA== BM6dDvGjjeFBDTN8BeDEVg==

This table suggests the limit of the average rates of change as t approaches 0.5 from the left is approximately XFnw9W4YV2DY62VqrYm0C8FUhMM= dollars per year (rounded to two decimal places).

2
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Question 1.12

Now calculate the average rate of change over three intervals to the left of t = 0.5. (Round your answers to four decimal places.)

Interval [0.49, 0.5] [0.499, 0.500] [0.4999, 0.5000]
Average rate of change bECI2HMu3zb8FISFiyvzAg== AqHQgaV4SHbsguD1jWG/hg== HZJ3TiwmXftPFf5AM9MwDw==

This table suggests the limit of the average rates of change as t approaches 0.5 from the left is approximately FB:*$avg499999toH dollars per year (rounded to two decimal places).

2
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Incorrect.

Question 1.13

Based on the previous questions, the instantaneous rate of change at t = 0.5 is approximately L1roKTQ32O/N3Yl8O0Zde3nASJA= dollars per year (rounded to two decimal places).

2
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Incorrect.