Math 124
x |1.0 |1.4 |1.8 |2.2 |2.6 | |
|[pic] |1.06 |2.2 |3.2 |2.8 |3.1 |
1. A function [pic] is continuous and differentiable with values given in the table at the right.
Use the values in the table to estimate the following
A. [pic] [pic]
B. [pic]
C. The average rate of change of [pic] between [pic] and [pic].
D. The rate of change of [pic] at [pic].
E. The equation of the tangent line to [pic] at [pic].
|x |12 |12.4 |13 |
|[pic] |2 |3 |3.5 |
2. The values of the derivative [pic] are given in the table:
Estimate the values of [pic]in the table below.
|x |12 |12.4 |13 |
|[pic] |8 | | |
3. Let [pic]. Estimate [pic] using a numerical approach. Give your answer to 4 decimal places.
4. [pic]. Find [pic] using an algebraic approach. Give an exact answer.
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